Let me try it one more time succinctly. And *then* I can get to the library.
I am not saying that the Buddha didn't teach rebirth as useful to practice. It is clear to me that he found that belief in rebirth was effective in moving people forward in his dhamma. But I am suggesting that he designed his lessons in a way that would lead followers who were ready for it past belief in rebirth, and that he was conveying that perceiving the world in terms of rebirth, while helpful to many, limits practice if taken in the direction that causes people to go looking for evidence of rebirth, working hard on finding the evidence, and perhaps even bending experience in support, to prove it to themselves rather than being able to work with just what is readily visible, and let go of views of the operation of self-and-cosmos, and the drive to find evidence to support those views.
So as far as my understanding of the first goal, everyone is, in my estimation, correct that he taught rebirth, but it was as a tool, not as something one should believe in. So far as my understanding of the second goal: whatever moves you forward in the dhamma is good.