This is really more of aporia about selfhood than a proof by contradiction against free will. I mean it is also the latter, but as a side effect.
Anyways the reason I'm saying this is that it has been discussed outside the West (where "free will" in itself is important, especially in Christian theology). For example, the entirety of the Indian philosophical traditions could be described as the questioning the nature of the self.
Buddhism is especially important here. The nature of the self is a tricky question with seemingly vague and contradictory answers. The self neither exists, doesn't exist, doesn't exist and not exist both, nor neither... rather it's a question not to even be answered.
I like these kind of aporetic topics. I believe that in Buddhism the real solution is to experience the truth of a matter personally ie. through meditative insight and enlightenment. Or maybe getting high.
Another way to put it is that it is a linguistic or cognitive issue that requires a perspective shift...maybe Wittgensteinian? That the concept of a self or free will is a limiting one that will lead to holes and contradictions in systems of logic, and are really more useful as a conventional marker for an abstraction. But not reality itself in itself