That aside, I'm saying that I don't see how non-physicality solves the problem of free will. In a physicalist interpretation decisions can be influenced by internal state, influenced randomly, or influenced by external forces. Non-empirical facts are still state. What additional factor does non-physicality contribute that I didn't list?
Is a 'soul' part of the person or external? Does it have state? Does it contribute randomness? What is it that it actually does except add something else we have to ask these questions about?
When you have a group of people "gathered together" ("In my name") there surely must be a subtle but coherent magnetic field that interacts with the physical to bring about "unexplainable phenomena". Perhaps the notion of God/gods could be explained this way.
Indo-european rune technology involves subtle magnetic fields in complex shapes, and are believed to affect the physical in "non-deterministic" ways as well. [1]
1. "Runelore" by Edred Thorsson
Only if you want to stay with reality not venture into phantasy.
We're starting from the position that we are not entirely sure how the physical world works. From that starting point, pushing the problem of free will off into some other metaphysical realm which we also don't fully understand solves no problems. Unless we can posit rules or mechanisms that apply to souls but that can't apply physically, and show what those are, they are philosophically indistinguishable.
Personally I'm very much in the compatibilist camp. For a decision to be mine, it must depend on my state. If the decision does not derive directly from my state (memories, personality, emotions, etc) then it is not my decision. So the extent to which a decision comes from some other source, to that extent the decision is not mine. Again punting the problem off to a 'soul' adds no conceptual value. Either the soul is part of me and part of my state, or it isn't.