I was reading your thread and find it interesting, although I spent some time really thinking about the possibilities of reincarnation and decided it was very difficult to know for certain. I would much prefer the idea to any other form of life after death, and so much could be learned through many lives rather than the restrictions of one body and one set of life experiences.
I originally began wondering about reincarnation as a child because one of my earliest memories was being in a cot, with one of my mother's friends offering me a biscuit. I had the thought 'I am coming round again'. It felt like a distinct waking up, not from sleep, but something more.
I was also compared a lot to my grandfather, who died 6 weeks before I was born and began wondering if I was a reincarnation of him.One particular strange experience which I had was looking for a fairly rare writer on school stories from an earlier time, and my mum telling me that there had been a copy of that book in my grandfather's books which she threw away. I never suggested the idea that I could be a reincarnation of him to anyone in my family because it was not an accepted belief. Of course, I realise that I may have read too much into a coincidence and built up a story in childhood, possibly as a result of my mother's projection of her loss of her father, so shortly before my birth.
One thing which I have wondered about in thinking about reincarnation memories, is if rather than people remembering specific personal memories, they are tapping into the collective unconscious of memories. However, I am aware that many people on this site find Jung's idea of the collective unconscious as rather unsound.
But, I do think that it is possible that we are individual beings of consciousness, interconnected with others in time. Perhaps, we all aspects of an underlying group mind. I am not speaking of consciousness as some abstract force, as the idealists describe, but as permeating nature. It could be that nature and consciousness is like a web.So, we may have some connection with previous lifeforms on some level, with some continuity between the generations.
I like to keep the idea of reincarnation as a matter for contemplation, as a possible way of seeing consciousness existing in other future lives. However, my own understanding is that the Buddha was uncertain about rebirth, so I like to keep an open mind.