So your belief in free will comes from "It's going to turn out to come from something really weird"? That's not convincing either.
I don't believe in free will, but I believe that there will always be the illusion because the computing needed to know anything before it happens is far too much, and if you knew, it would add another layer of things you'd need to compute, meaning you still wouldn't know your choice ahead of time.
I agree that the infinite regress argument is not convincing - it proves nothing. I would point to science, physics, etc, which is much more factually supportive of it. Of course you can point out quarks, quantum computing, etc, but my argument is that the "randomness" is simply a system we have yet to understand.
More importantly, you highlight something else - choice is not the same as free will. Yes, we all have choices we make every day. They seem to be our will because we don't understand how they were made down to the particles. Whether or not there is free will, there is always choice. So the question is, when is the lack of free will actually relevant? I find that a lot of people apply it in ways that don't make sense when it actually does offer insight in certain interesting areas such as ethics.