You are assuming your conclusion. If free will exists, it might exist outside the current understanding of physics. Most likely, it does (if it exists!)
I did address dualism. I'm not making any assumptions about whether dualism is true or not. If dualism is true, the immaterial part is just another form of state that is part of the self from which the decision emerges.
Physics assumes the conclusion. If free will exists (which it appears to), it must exist within the contingencies of physics. To assume otherwise it to say that you don't like physics.
