As a neo-objectivist, I will try to address your confusion, as this also confused me in the past. The core problem is the difference between the concepts of altruism and benevolence. Altruism is an ethical code that advocates sacrificing one's self-interest for the welfare of others, considering it the standard of the good. On the other hand, Benevolence is the virtue of being selectively kind and respectful to others according to egoistic consideration by desiring their well-being to obtain a peaceful, cooperative relationship with them. While both concepts involve consideration for others, benevolence is fundamentally different from altruism as it does not require sacrificing one's values or living for the approval of others; benevolence is an 'otherness' that is mutually beneficial to the self and one's happiness according to one's values, done without guilt or pity.
In your essay, you discuss examples of benevolent actions that might appear to lack direct compensation but are actually motivated by individuals recognizing positive aspects of themselves in others and desiring a relationship with them, even without immediate benefits.
The confusion between benevolence and altruism is quite common among readers of Ayn Rand as she never wrote an essay on the subject, only briefly mentioning how altruism was not benevolence, such as in a 1964 Playboy interview:
"It is altruism that has corrupted and perverted human benevolence by regarding the giver as an object of immolation, and the receiver as a helplessly miserable object of pity who holds a mortgage on the lives of others—a doctrine which is extremely offensive to both parties, leaving men no choice but the roles of sacrificial victim or moral cannibal."
Ayn Rand does not directly elaborate on this distinction because she contextualizes them under the framework and virtue of justice and judging when to provide charity. Her own standard provides insight into benevolence:
"The proper method of judging when or whether one should help another person is by reference to one’s own rational self-interest and one’s own hierarchy of values: the time, money or effort one gives, or the risk one takes should be proportionate to the value of the person in relation to one’s own happiness. To illustrate this on the altruists’ favorite example: the issue of saving a drowning person. If the person to be saved is a stranger, it is morally proper to save him only when the danger to one’s own life is minimal; when the danger is great, it would be immoral to attempt it: only a lack of self-esteem could permit one to value one’s life no higher than that of any random stranger. (And, conversely, if one is drowning, one cannot expect a stranger to risk his life for one’s sake, remembering that one’s life cannot be as valuable to him as his own.) If the person to be saved is not a stranger, then the risk one should be willing to take is greater in proportion to the greatness of that person’s value to oneself. If it is the man or woman one loves, then one can be willing to give one’s own life to save him or her – for the selfish reason that life without the loved person could be unbearable.
David Kelley also delves deeper into this subject in his book 'The Unrugged Individualism' and in his talks on justice and benevolence, which you can watch here.
Another misunderstanding is that, as you note, Ayn Rand does not use selfishness the same way conventional people do, which makes understanding her a bit annoying, but this seems to be more of a failing on your end than hers, as she makes this point very clear in The Fountainhead and Atlas Shrugged. As Kalciphoz's comments pointed out, her villains are selfless because they have no sense of self, and while their actions might seem to benefit them, they are living for others. I brought up the concept of benevolence because you can mentally replace altruism with benevolence, and it would solve your mental contradiction; this need for another word of 'otherness' that is similar to altruism but isn't altruism seems to be the key problem in your mind.
Tying it back to fiction: Ayn Rand's heroes never surrender a greater value for the sake of a lesser one or of a nonvalue, but they always act selectively kind and respectful to others according to egoistic consideration by desiring their well-being to obtain a peaceful, cooperative relationship with them. Don't be an altruist, be benevolent towards others you value and see value in because it ties back to your own happiness.
I.
An unfortunate obstacle to appreciating the work of Ayn Rand (as someone who adores the "sense of life" portrayed in Rand's fiction, while having a much lower opinion of her philosophy) is that when Rand praises selfishness and condemns altruism, she's using the words "selfishness" and "altruism" in her own idiosyncratic ideological sense that doesn't match how most people would use those words.
It's true that Rand's heroes are relatively selfish in the sense of being primarily concerned with their own lives, rather than their effects on others. But if you look at what the characters do (rather than the words they say), Rand's villains are also selfish in a conventional sense, using guile and political maneuvering to acquire power and line their own pockets, while claiming to be acting for the common good. For example, in Atlas Shrugged, the various directives ostensibly issued for the economic health of the country are seen to instead benefit politically connected crony capitalists like James Taggart and Orren Boyle. In Think Twice, the philanthropist Walter Breckenridge cultivates a public image as an inventor and benefactor of humanity while stealing credit for his junior partner's work and deriving gratification from exerting power over the people he "helps".
Despite paying lip service to a pretense of only trading and never giving, we also see examples of Rand's heroes being altruistic in the conventional sense, of being motivated to help others. For example, in Atlas Shrugged, Hank Rearden rearranges his production schedule (at a critical time when he could scarcely afford to do so) in order to sell steel to a Mr. Ward, who needs the steel to save his family business (but doesn't see Rearden as obligated to help him). Rearden's motive is pure benevolence: "It's so much for him, thought Rearden, and so little for me!" Giving What We Can couldn't have chosen a better slogan.
Overall, when I look at the universe portrayed in Rand's fiction, it seems to me that the implied moral isn't that altruism is bad.
It's that altruists don't exist. The people claiming to be altruists are lying. The distinguishing feature of our heroes isn't, actually, that they're unusually selfish. It's that they're honest about being mostly selfish, and that they want to pursue their interests within a framework of rights that respects that other people are also trying to pursue their interests. "I swear by my life and my love of it that I will never live for the sake of another man, nor ask another man to live for mine," goes the motto of the striking heroes of Atlas Shrugged (emphasis mine); the second clause is important. Given that everyone is mostly selfish and everyone has to eat, the question is: are you going to eat by means of production and trade, or by—other means?
That's the distinction between Rand's heroes and villains. The heroes want to get rich by means of doing genuinely good work that other people will have a genuine self-interest in paying for. The villains want to wield power by means of psychological manipulation, guilt-tripping and blackmailing the people who can do good work into serving their own parasites and destroyers.
As Greg Hastings, the district attorney in Think Twice, puts it: "[T]he man who admits that he cares for money is all right. He's usually worth the money he makes. He won't kill for it. He doesn't have to. But watch out for the man who yells too loudly how much he scorns money. Watch out particularly for the one who yells that others must scorn it. He's after something much worse than money."
Furthermore, the heroes know that wealth and fame acquired by fraud obviously "don't count." In The Fountainhead, Peter Keating's outwardly successful architecture career has been a sham: he social-engineered his way into partnership in his firm, and all of his best work was plagiarized from the hero, Howard Roark. The turning point for Keating's character is when he asks Roark to let him plagiarize his work one last time, for the Cortlandt housing project, which Roark would never be allowed to work on for political reasons. Keating finally realizes that fraudulent "success" in the eyes of others is no success at all:
In summary, the ultimate sin in Rand's moral universe isn't giving charity. (Because, within the ideology, helping those others whom you want to help, is selfish.) What's evil is demanding charity, claiming the unearned, expecting other people to work for your benefit because you supposedly need them to.
II.
Something people have occasionally noticed about my intellectual style is that I like to win arguments. I take pride and pleasure in pointing out flaws in other people's work in the anticipation of the audience appreciating how clever I am for finding the hole in someone's reasoning.
The people pointing out this fact about me generally seem to think it's a bad thing. They tell me that I should be more charitable to the viewpoints of others, that I ought to be doing collaborative truth-seeking.
It's true, of course, that there's a terrible danger in wanting to win arguments. Once your conclusion has been determined, coming up with more arguments for it can't make you more correct, even if it can help you "win" a debate. Learning something entails changing your mind, which people are often reluctant to do because it amounts to "losing".
A useful heuristic for overcoming this bias against being willing to "lose" arguments is to take heed of a "principle of charity", of taking the strongest and most rational interpretation of others' words. The person you're arguing against is trying to do what they think is right. If you end up disagreeing with them, it shouldn't be because they're stupid and evil; your theory about why the other person is getting the wrong answer shouldn't make them look that bad. If it does, that's a sign that you haven't really understood their point of view and therefore can't claim to have justly refuted it.
From the standpoint of ideal epistemology, however, the "principle of charity" is not a principle, and the idea of "charity" itself is irrelevant or incoherent. Normatively, theories are preferred to the quantitative extent that they are simple and predict the observed data. There is no concept of a theory "belonging to" someone, or favoring someone's interests.
For contingent evolutionary-psychological reasons, humans are innately biased to prefer "their own" ideas, and in that context, a "principle of charity" can be useful as a corrective heuristic—but the corrective heuristic only works by colliding the non-normative bias with a fairness instinct, effectively playing the bias against itself: you wouldn't like it if someone dismissed "your" ideas without understanding why they appeal to you, goes the thought, so you should extend the same consideration to others.
Normatively, of course, this is nonsense. You should update on an interlocutor's arguments for the same reason that a scientist working alone would update on the results of an experiment: because (and to the extent that) the result conveys information about reality. We would not speak of being charitable to an experimental apparatus. The scientist is not doing their lab equipment a favor.
Because the principle of charity is merely a corrective heuristic for the bias of arbitrarily favoring "one's own" ideas, it correspondingly only makes sense to apply in one direction—as a corrective for one's own thoughts. I tell myself to make a special effort to look for reasons why I might be wrong and my interlocutor is right because, knowing what I do about human nature, I selfishly expect to thereby achieve more accurate beliefs than I would in the absence of the special effort. It's a workaround, a mitigation for a known bug in human cognition; it makes sense whether or not the other person reciprocates, and whether or not I'm particularly trying to collaborate with them.
On the other hand, when someone who is currently trying to persuade me of something tells me that it doesn't look I'm making enough effort to think of reasons why they're right, that immediately makes me think they're more likely to be wrong. Why? Because I think that if they had an argument, they would be telling me the argument, not chastising my lack of charity. The advice to be on special lookout for reasons your interlocutor is right is good in general, but your interlocutor is the last person to be trusted to give it, because (due to the warp in human psychology) they have an ulterior motive.
Overall, when I look at the world of discourse I see, the moral I draw is not that that collaborative truth-seeking is bad.
It's that collaborative truth-seeking doesn't exist. The people claiming to be collaborative truth-seekers are lying. Given that everyone wants to be seen as right, the question is: are you going to try to be seen as right by means of providing valid evidence and reasoning, or by—other means?
Or to put it another way: the commenter who admits they care for status is all right. They're usually worth the status they earn. They won't lie for it. They don't have to. But watch out for the commenter who yells too loudly how much they scorn status. Watch out particularly for the one who yells that others must scorn it. They're after something much worse than status.
Furthermore, I know that "winning" a debate via sophistry and rhetorical tricks obviously "doesn't count." Maybe I could fool an undiscriminating audience, but I would know it wasn't real.
Sometimes I want people to understand some specific truth (out of the vast space of possible truths to pay attention to), for selfish reasons of my own. In these cases, I'm happy to do the work of explaining to put it on the shared map. When someone asks me questions about my work, I don't regard it as an attack, because I expect to be able to answer them—and if I can't, that's my problem.
I will never ask my interlocutors to be more charitable to me. I will often say "That's not what I meant", or "That's not a reasonable interpretation of the text I published"—but that's a claim about what I mean, or a claim about the text; it's not a claim on them. I don't expect people to listen to me because I supposedly need them to.
III.
My favorite scene in Atlas Shrugged is the one where Cherryl Taggart (née Brooks) goes to see Dagny Taggart after discovering the truth about her marriage. Cherryl had married Dagny's brother James thinking that he was the intrepid industrialist responsible for the success of the Taggart Transcontinental railroad, only to later find out that James is a phony political actor who took credit for Dagny's accomplishments after the fact, despite having opposed her initiatives and made her work more difficult.
("I married Jim because I ... I thought that he was you," Cherryl tells Dagny. There is some very beautiful slash fanfiction that needs to be written picking up from that line, which is out of scope for this blog post.)
Cherryl intends only to briefly apologize to Dagny for earlier insulting remarks, not to make any further imposition—and is surprised when Dagny not only forgives her, but seems to take a genuine interest in her welfare. It's worth quoting at length: