I think you're on the right track to say that there are all sorts of types of pleasures, and some occur with the removal of pain, and some occur when we shift our attention from one pleasure to another.
As I understand it a classic example of a pleasure that is not a removal of pain or want is that of smelling a rose. The smell does not necessarily remove a pain, and we weren't "in lack of a good smell" before smelling it. Our attention turned from one pleasure to another without any removal or displacement of any sort of pain.
Again I think we generously acknowledge that there are all sorts of pleasures, without ever flipping all this on it's head by saying that the goal is "absence of pain." The goal is technically only "absence of pain" from a very very limited perspective - when we are talking about the total quantity of human experience and we're observing that we want the totality of experience to be pleasure(s) with as little pain(s) as possible (preferably, but perhaps not practically for a human, zero).