If I'm trying to reason about counterpossibles (or impossible possible words) then the usual laws of logic and proof just fly out of the window. I can't legitimately infer from A -> B and A-> ~B that ~A.

In our models so far, this isn't a problem, you just use a factory-standard first order inference system. What do you mean by "can't legitimately infer"? The worst that can happen is that you infer something misleading (but still valid), and the diagonal step/chicken rule is one way of ensuring that doesn't happen.