Have you written anywhere about the issue of physical determinism not undermining rationality, as Anderson mentions in this post? Isn't the truth of that contention the essence of Lewis' argument in Miracles and Reppert's Argument from Reason?
There's a difference between physical determinism that's driven by a "blind watchmaker," and physical determinism that's driven by a sighted watchmaker. The problem with physical determination in naturalism is that the end-result is the product of mindless factors. It's not the physical aspect or the deterministic aspect that undermines reason. An electronic calculator is reliable because it was designed by an intelligent agent. As a theory of mind, physicalism is beset by its own problems. But that's additional.