Naturalism (as we currently understand the laws of nature) doesn't totally imply determinism. There is some quantum uncertainty at the lower layers. But that isn't the same as me having free will, because my free will doesn't control the quantum uncertainty.

As for compatibilism... it looks like "you can't totally prove that materialism implies no free will, so it might be possible." No mechanism, not even a guess at one, just "it could still be". Forgive me, but I don't find that very persuasive.

I think that my objection to most of the compatibilism stuff is this: What is the "I" that is going to choose? In a purely naturalist view, all I can be is a collection of matter that obeys the laws of physics, because there's nothing else for me to be. I'm a machine made out of atoms, nothing more. It seems to me that all these compatibilist arguments aren't really taking that seriously. (Perhaps not surprisingly, since they're being made by philosophers, not physicists.) They therefore have some intuitive, experience-based idea of what a person is that sneaks in to their arguments, rather than really grappling with the implications of the purely naturalist position.