I'm not sure how you're getting from not provable(X) to provable(provable(X) -> X), and I think you might be mixing meta levels. If you could prove not provable(X), then I think you could prove (provable(X) ->X), which then gives you provable(X). Perhaps the solution is that you can never prove not provable(X)? I'm not sure about this though.
I forget the formal name for the theorem, but isn't (if X then Y) iff (not-x or Y) provable in PA? Because I was pretty sure that's a fundamental theorem in first order logic. Your solution is the one that looked best, but it still feels wrong. Here's why: Say P is provable. Then not-P is provably false. Then not(provable(not-P)) is provable. Not being able to prove not(provable(x)) means nothing is provable.
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