>but that observation isn't relevant to the mental processes of Alice and Bob

Sure. From their context, they may not be able to distinguish which is correct. But that doesn't mean it doesn't matter. When that context changes (eg. they learn something new), it matters a lot, and it's pretty relevant to their future actions and predictions. Thus it's an important aspect we want to distinguish in our epistemology. Ie. if Bob learns he was wrong, he shouldn't think his new situation is just as good as his old one just because in both cases he held "the best beliefs that can be constructed on the basis of his evidence". Something meaningful has been said, and that difference is important to encapsulate when discussing epistemology.

This distinction is independent of the internal belief states, but that's exactly why it's so important: we don't just want to talk about internal states, we want to relate these to the external reality we're talking about. The world where my belief is wrong is different in a very important way from a world where it's correct - a way I care very much about.

>Saying that Bob knew ¬X and lost that knowledge when he changed his belief centers our assessment of Bob's mental processes on the wrong thing

This is the wrong faming though. Bob never knew ¬X: ¬X was false. He thought he knew ¬X, but was mistaken. And that mistakenness is something Bob would care about, and should consider meaningful to his epistemology. If he didn't care about his truth, it'd be just as good for him to avoid learning anything, because he'd be in the same state either way wrt holding a reasonable belief. But in reality, if he's wrong, he'll want to find this out, and consider his situation improved when that happens.

>what Bob should be concerned with is what conclusions he can draw on the basis of his available evidence

The reason Bob should be concerned with this is solely because Bob wants his beliefs to be true ones. You can't discard that aspect.

>Perhaps another way of stating this would be to say that Bob ought to believe he knows X as a result of {A, B, C}, and that whether he knows X (or that he cannot know X because ¬X is true) is irrelevant.

Bob ought to believe X, but that certainly doesn't mean whether he knows it is irrelevant - epistemic contexts can change, and ones where our beliefs reflect truth are more valuable to us than ones that don't.