I'm afraid the information you detail in the rest of your post doesn't demonstrate that, though. I've heard the same stuff--didn't they make the movie Little Budha about this? (didn't see that movie)--but I've never seen any convincing documentation--it's always some Buddhist said so, and such.
Reincarnation is bunk, but some people want to believe it, and the passionate belief seems to be the "proof". (Not putting you in that category.)
That's certainly what this scientifically educated FReeper used to think; and maybe I still do, I'm not sure. Read Life Before Life by Jim Tucker, also scientifically educated and associated with the University of Virginia.
ML/NJ