If skepticism about free will renders the EA endeavor void, then wouldn't it also render any action-guiding principles void (including principles about what's best to do out of self-interest)? In which case, it seems odd to single out its consequences for EA.

You sometimes see some (implicit) moving between "we did this good thing, but there's a sense in which we can't take credit, because it was determined before we chose to do it" to "we did this good thing, but there's a sense in which we can't take credit, because it would have happened whether or not we chose to do it", where the latter can be untrue even if the former always true. The former doesn't imply anything about what you should have done instead, while the latter does but has nothing to do with skepticism about free will. So even if determinism undermines certain kinds of "you ought to x" claims, it doesn't imply "you ought to not bother doing x" — it does not justify resignation. There is a parallel (though maybe more problematic) discussion about what to do about the possibility of nihilism.

Anyway, even skeptics about free will can agree that ex post it was good that the good thing happened (compared to it not happening), and they can agree that certain choices were instrumental in it happening (if the choices weren't made, it wouldn't have happened). Looking forward, the skeptic could also understand "you ought to x" claims as saying "the world where you do x will be better than the world where you don't, and I don't have enough information to know which world we're in". They also don't need to deny that people are and will continue to be sensitive to "ought" claims in the sense that explaining to people why they ought to do something can make them more likely to do it compared to the world where you don't explain why. Basically, counterfactual talk can still make sense for determinists. And all this seems like more then enough for anything worth caring about — I don't think any part of EA requires our choices to be undetermined or freely made in some especially deep way.

Some things you might be interested in reading —

• Harry Frankfurt: Freedom of the will and the concept of a person
• Harry Frankfurt: Alternate possibilities and moral responsibility
• P. F. Strawson: Freedom and responsibility
• Kathleen Vohs & Jonathan Schooler: The Value of Believing in Free Will: Encouraging a Belief in Determinism Increases Cheating

I think maybe this free will stuff does matter in a more practical way when it comes to prison reform and punishment, since (plausibly) support for 'retributive' punishment vs rehabilitation comes from attitudes about free will and responsbility that are either incoherent or wrong in a influencable way. 

According to the PhilPapers survey, over half of philosophers favour a compatibilist approach to free will - i.e. that free will is compatible with determinism.

I also recommend the LessWrong writing on the subject.

“If free will doesn’t exist, does that ruin/render void the EA endeavor?”

Well, what does it matter if free will exists? Even if free will doesn’t exist, my life circumstances have led to me becoming invested in improving the world by engaging in altruism. My brain’s reward circuitry is still aligned with doing the most good that I can do for as long as I am able. I think for most of us who identify as altruists, the tendency to help those who need help is not tied to the idea of free will. I suppose that there are people who would take the absence of free will to be a pass to stray from altruism, but I doubt you’ll find them in the EA community.

Personally, losing my belief in free will has had a big, big difference in how I see the world. Because I believe free will doesn’t exist, I cease to judge those who are on the bottom rungs of our society. I have a deeper compassion for people who have addictions, who have committed crimes, who are not the easiest to care about. I have more patience with those who have differing opinions, even with flat-earthers and religious fundamentalists.

Shedding my belief in free will also helped me be kinder to myself. I am more patient whenever I face challenges arising from my shortcomings. I forgive myself for my failures and try to be humble even in my triumphs. My prime motivation to make the world a better place is no longer guilt but rather a genuine pleasure in spreading kindness. 

In so many different ways, not believing in free will has made me a better altruist and a kinder friend to myself. I hope questioning free will does the same to you!

I'm no expert in this topic and haven't read Sam Harris's argument, but there are a couple of things I usually bear in mind:

1. If you're uncertain about whether determinism is true (that is, the probability you assign to hard determinism is less than 1), then it seems you should still act as though you are not determined.  Then we can apply reasoning like Pascal's Wager -- if determinism is false, then sadistic torture is terrible; if it's right, then we are indifferent.  Hence it seems that we should still act on the side of morality still having bearing.

2. A more compelling response (although, still contentious) is compatibilism.  I leave you to explore it here.