I think the error is that you didn’t prove it was unprovable—all provably unprovable statements are also provable, but unprovable statements aren’t necessarily true.
In other words, I think what you get from the Deduction Theorem (which I’ve never seen before, so I may have it wrong) is Provable((Provable(C) → C) → C). I think if you want to “reach inside” that outer Provable and negate the provability of C, you have to introduce Provable(not Provable(C)).
I think the error is that you didn’t prove it was unprovable—all provably unprovable statements are also provable, but unprovable statements aren’t necessarily true.
In other words, I think what you get from the Deduction Theorem (which I’ve never seen before, so I may have it wrong) is Provable((Provable(C) → C) → C). I think if you want to “reach inside” that outer Provable and negate the provability of C, you have to introduce Provable(not Provable(C)).