I think a lot of the asymmetry in intuitions just comes from harm often being very easy to cause but goodness generally being very hard. Goodness tends to be fragile, such that it's very easy for one defector to really mess things up, but very hard for somebody to add a bunch of additional value—e.g. it's a lot easier to murder someone than it is to found a company that produces a comparable amount of consumer surplus. Furthermore, and partially as a result, causing pain tends to be done intentionally, whereas not causing goodness tends to be done unintentionally (most of the time you could have done something good but didn't, probably you had no idea). So, our intuitions are such that causing harm is something often done intentionally, that can easily break things quite badly, and that almost anyone could theoretically do—so something people should be really quite culpable for doing. Whereas not causing goodness is something usually done unintentionally, that's very hard to avoid, and where very few people ever succeed at creating huge amounts of goodness—so something people really shouldn't be that culpable for failing at. But notably none of those reasons have anything to do with goodness or harm being inherently asymmetrical with respect to e.g. fundamental differences in how good goodness is vs. how bad badness is.

The title of the post says negative utilitarianism is more intuitive than we think, but the body of the post says the intuitions behind negative utilitarianism make sense.

There is a critical distinction between these two claims. Indeed, the whole point of the seemingly endless philosophical debates over the fundamental nature of ethics^[1] is that you can start with seemingly reasonable assumptions, but reach crazy conclusions. And you can also start with different, but just-as-reasonable assumptions^[2] and reach completely contrary conclusions. 

The resolution to this seeming paradox is that our intuitive sense of "reasonableness" contains fundamental, irresolvable contradictions inside of it. Contradictions that^[3] do not matter too much in mundane/prosaic areas we're familiar with, but which get amplified when the tails come apart and stuff like uploading, mass population increases, etc, become available. There is some connection to the notion of "philosophical crazyism" mentioned in this comment by Carl Feynman.

In math and logic, there is something known as the principle of explosion. It says that as long as you have at least one contradiction between your axioms, you can apply rules of inference to prove all statements inside your system are both true and false. Even the slightest problem can get amplified and break the whole edifice down. Something analogous seems likely to happen to our ability to handle the moral conundrums around us, if stuff gets wild sometime in the future.

I have written more about these kinds of topics here.

1. ^{^}

   Or, frankly, most philosophical debates, regardless of topic

2. ^{^}

   Stuff like "increasing the total amount of happiness in the world is good, all else equal" or "making people happier is good, all else equal"

3. ^{^}

   As basic evo-psych would predict

If you haven't seen it already, you might find The Case for Suffering-Focused Ethics of interest. Like your article, it collects various intuitions that many people have that might push them toward a view that puts special priority to the prevention of suffering over the creation of pleasure. Your examples remind me a bit of the "Two planets" thought experiment listed on that page (though their focus is slightly different):

Two planets

Imagine two planets, one empty and one inhabited by 1,000 beings suffering a miserable existence. Flying to the empty planet, you could bring 1,000,000 beings into existence that will live a happy life. Flying to the inhabited planet instead, you could help the 1,000 miserable beings and give them the means to live happily. If there is time to do both, where would you go first? If there is only time to fly to one planet, which one should it be?

Even though one could bring about 1,000 times as many happy beings as there are existing unhappy ones, many people’s moral intuition would have us help the unhappy beings instead. To those holding this intuition, taking care of suffering appears to be of greater moral importance than creating new, happy beings.

It's worth distinguishing between negative utilitarianism and merely having suffering-focused ethics. NU is an special case of SFE, where "suffering-focused ethics is an umbrella term for moral views that place primary or particular importance on the prevention of suffering". So it sounds to me like a reasonable claim that

And though most cannot be described as actually following any particular named ethical theory, I think a reasonable approximation for many people’s ethical view is that they:

• Have a (non-normative) preference to personally feel happy/have positive experiences
• Have a (non-normative) preference for others to feel happy/have positive experiences, usually centered on their family, close friends, and other personal acquaintances
• Believe it’s immoral to cause harm/pain/suffering to others, where the more suffering, the worse the sin

That is, their moral beliefs (rather than their personal preferences) mostly relate to reducing the negative rather than increasing the positive.

But I think it's not very productive to describe this as something like "NU, just not taken to extreme lengths such as destroying the worlds". The defining feature of NU is that it puts zero intrinsic weight on positive experiences. If you have a theory that does include a preference for people to experience positive experiences, but just puts a higher weight on preventing suffering than it does on making people have positive experiences, then that theory is something different than negative utilitarianism. So it'd be clearer to call it something like a "suffering-focused" theory instead.

At least judging by their other stated normative beliefs, most people:

...

Would not agree that it’s immoral to fail to create more positive experiences (or reduce the amount of positive experience someone has)

One example of "creating more positive experiences" is giving your children a happy childhood full of joy vs. a merely indifferent one full of drab. Would "most people" really think that there is no duty to do the former and avoid the latter?

Seems like a mistake to write these intuitions into your axiology.

The following thought experiment by Tim Scanlon is also a relevant example (quote from Edmonds's Parfit):

Suppose that Jones has suffered an accident in the transmitter room of a television station. Electrical equipment has fallen on his arm, and we cannot rescue him without turning off the transmitter for fifteen minutes. A World Cup match is in progress, watched by many people, and it will not be over for an hour. Jones’s injury will not get any worse if we wait, but his hand has been mashed and he is receiving extremely painful electrical shocks. Should we rescue him now or wait until the match is over?