Dear Cristi,
You say "at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.
Thus I see no reason to contend that free will is isomorphic to math. Even if one can, post exercise of free will, or even concurrent with the exercise of free will, find some neural correlates. Free will partakes of causal and I don't think mathematics reaches causal. So I don't think "everything is isomorphic to a mathematical structure." You seem to think differently. With reference to time, you say, "there is no conflict between mathematics and causal explanations." But I don't believe there is an 'explanation' for free will. I don't see this as in conflict with your arguments about a theory of everything, to the effect that we cannot be living in a world described by two disconnected sets of laws. That seems to me a self-consistency argument that does not depend upon everything being isomorphic to math.
On another point you note "if it looks like a duck, swims like a duck, and quacks like a duck, then it is a duck, isn't it?"
My essay analyzes why John Bell thought that "it looked like Dirac spin, behaved like Dirac spin, and had an eigenvalue equation like Dirac spin, ['it' being the Pauli eigenvalue equation.] I argue that the Pauli equation of Stern-Gerlach is not the Dirac equation of relativistic QM, and that Bell's oversimplification of this led him to impose what he felt were reasonable constraints that prevent a local model from achieving QM correlations.
I hope you will read my essay and comment.
My best wishes to you,
Edwin Eugene Klingman