We have empirical proof of materialism from experiments showing that manipulating the brain with drugs, electrical stimulation, and lobotomy affect what it thinks. In the same way, we have proof of materialism for computers.
That does not tell us much about how causality follows or make statements about objective reality. Definitively it only shows that one conscious agent influenced another conscious agent’s (or own) state.
You're introducing an unnecessary concept. We know the physical brain is doing the thinking, and we know that it can be manipulated physically. Throwing in metaphysics just for shits and giggles is like saying we don't know how much physics controls the motion of the stars and that there could be metaphysics involved there as well. Good luck telling physicists that they don't need to search for dark matter because everything can be explained with magic.
Why do you think this in some way interferes with physics? Philosophical views could inform natural sciences but they don’t invalidate them.
Non-materialist philosophy is very compatible with physics. The problem is people who start talking physics as philosophy/religion and believe that metaphors in current physical models (electrons flying, strings vibrating, fields permeating) are not metaphors but actual final objective reality, thinking that natural sciences make existential statements.
Natural sciences do not allow for free will. It's really not that hard. The brain thinks, and it does so by following physical processes just like a digital computer. Only when you bring in metaphysical mumbo jumbo do you run into the kinds of problems you're having.
Natural sciences do allow for free will. To be more precise, natural sciences do not concern themselves at all with non-falsifiable theories about whether free will exists, what is “real reality”, and the like.
You are, of course, free to make such statements—but you shouldn’t try to pretend that physics backs it up, because it doesn’t. With these theories you are engaging in philosophy, and as long as you refuse to acknowledge that it will be difficult to discuss them with you constructively.