I agree with you that we can't resolve it, but I don't see how your proposal could be a possible way.
In terms of logic, there has to be a problem with accepting choice and determinism.
I can see where materialism can coexist with free choice, as we may not have all the facts about the rules which govern physical things. Or, cause and effect could apply to material things, and my will could be something not material. But, as I accept the fact that I am choosing (I do), I am denying in the process the possibility of determinism.
I might seem like a religious nut to some of you for believing I am free to choose. Yet, denying that I can choose requires more 'faith' than I have. In other words, I have more faith in my own experience and my senses (which is all I really have to go on) than I have in an unproven theory.
I can assent to the idea that these things could coexist for reasons that are beyond my capacity to understand. But, I can't concede that anything I've ever seen begins to make it seem remotely possible, including your attempts here, though I appreciate the effort.
There may be unknown resolutions; on this we can agree.