There are two save points in the Desert Palace! One is in the room where you solve a puzzle with Cid (return to the room after solving the puzzle). The other is in the room to the left of the one with three bookshelves stacked on top of each other.

As for the back-and-forth, yeah, that's a bit annoying. Then again, that sort of thing is pretty common in RPGs, I feel xD At least it's not that long!