I've tried unarchiving and re-archiving, but no luck getting it off the budget page.

When archiving a category, the expected behavior is for the category to no longer show up on the Budget and Overview pages. This only takes place from the next month onwards. Instead, considering there is no set budget or transactions assigned to the category for the current month, the change should apply immediately and the category should be hidden from the Budget and Overview page for the current month as well.