Do we really want even more quirky shibboleths that can be worn as attire without having to actually learn anything difficult and useful?
There's two very different reasons to say phrases, and your suggestions here are for something different than the circumstances you say "Good luck" in.
Sort of similar to the phrase "What's up?" or "How are you doing?" - the purpose is not to respond with a detailed (or even short but accurate) explanation of how you're doing. You're supposed to say "fine, you?"
You're not exchanging information, you are engaging in a short social bonding ritual in which you acknowledge each other's presence and familiarity before either moving on (either to a real conversation, small talk, getting down to some particular task, or parting ways). On special occasions, when it's the right time, you might actually inquire "Hey, how have you been doing lately? Haven't seen you a while?" and then one would respond with a serious, informative answer.
Similarly, "Good luck" is not (usually) a heartfelt thing you say to earnestly convey how you wish someone to do, it's a reflexive thing you say in the midst of a complex social situation. When you do want to earnestly convey a heartfelt wellwishing, you probably want to take the time to come up with s...
Should you also stop saying "goodbye" since the origin of the word is 'God be with you?' Or stop called celestial bodies "planets" because they do not in fact 'wander?' Good to be rational, less good to enshrine rationality against contamination by humanity and language and culture and history.
Here is a rational take on luck (4 page PDF, recommended)...
http://richardwiseman.files.wordpress.com/2011/09/the_luck_factor.pdf
If you don't have anything constructive to say to a person and want to signal wishing their success I think good luck works just fine.
Either way, if the receiver is another "rationalist", they will understand, and if not, don't try to freak out the normals.
"Deserve your luck by exploiting it."
Inspired from:
If we succeed in recalling a formerly solved problem which is closely related to our present problem, we are lucky. We should try to deserve such luck; we may deserve it by exploiting it.
-George Polya, How to Solve It.
I love the inversion. You can deserve your luck post hoc, not just a priori.
My favorite intellectually is "choose well," but I haven't successfully used it much because in the moment it sounds too ominous.
"Godspeed"? :-)
I suggest not worrying about it and just using "Good luck". I doubt the gods of rationality will punish you for it.
"Success." I picked it up after watching an English movie with Dutch subtitles. That's how they translated "Good luck."
"Do your best!"
(I'll only actually say "Ganbatte, ne!" if the other person is geeky enough to appreciate it.)
Well, if the goal is to imply the possibility of failure and the desire that they succeed, in some circles "Strike the earth!" would suffice.
"Good luck" isn't particularly irrational. There is indeed such a thing as luck -- external things working to your favor or not. (Rationalists, like everyone else, hopes that these things work in our favor.)
The phrase can be sort of unempowering though, so "kick some ass", "knock 'em dead", etc. can prove better encouragement at times, as well as longer, more sincere encouragement.
In sufficiently selective venues, I've been known to say "Good skill!" and "May the random variables be in your favor!"
I don't think there is anything wrong with "good luck." It doesn't imply any sort of belief in superstition, really. It just acknowledges that there are a number of effectively random things that influence success/failure.
"Make good choices."
Edit: Just realized this is pretty similar to the "Choose well" listed below, although it DOES sound a lot less ominous. And I think it functions as a universally applicable catchphrase that it's okay to use reflexively.
"Stay sharp"?
It doesn't mean the same thing, but it seems to fill the same conversational role.
Figure out what you actually mean then just say that. My suggestions are "may you succeed" or "I hope you prosper".
The Young Wizards series has "Dai stihó", a greeting in The Speech between wizards. It's simplest translation into english is "go well" but it also contains senses of "good luck", "do your best", "behave morally" and "be what you are".
"May your plans come to fruition"
I used to say that more when leaving megameetups or going on a trip or something. It has the disadvantage that you can't say it very fast.
I also want a word/phrase that expresses sympathy but isn't "sorry".
The phrase seems to express preference for the positive outcome, which in turn can be taken to mean that you'd be seeking a way of bringing it about. This seems to require some actual help with the problem or giving incentive for it to get solved. For a sufficiently hard problem, that might take the form of donating money to the problem-solving effort or setting up a prize for success.
I actually say "good luck" pretty generally (you can never have too much luck). If you're referring to specific action they're about to undertake and you want to emphasize hard work, "Make it so" is another situationally useful phrase.
Slightly more generally useful might be "Make the future happen."
Is your goal to increase the emphasis on hard-work and rationality, or just have something that sounds nice that you don't disagree with? (In that case I'd just go with "good luck").
This paragraph might come in handy. Why not attempt to raise motivation by inducing mental contrasting? "From where you are standing, work hard and you will get where you want to be" is a bit long, but seems like a good idea to me.
Is there any rationalist equivalent of "good luck"? I've tried a few variants, such as "work well", "knock them dead", "we're with you" and certain situation-specific phrasings, but haven't found anything that worked generally - though a hearty "may all the gods of Olympus be with you!" can serve. Not a vitally important point, but it would be nice to have something similarly supportive and yet accurate to say.