Thoughts on Single-Consciousness Time-Travel Reincarnation as a Really Cool Idea

Some religions (it's usually religions, isn't it?) say reincarnation happens. You die, and then your soul or whatever comes back in another living thing, maybe a person, maybe not, and you live again. I gather they say you generally have little or no conscious memory of previous lives. As I understand it, they preserve normal time-ordering, so that you're re-born AFTER you die.

I love Back to the Future and many other time-travel stories and related ideas in science, so sometimes I've thought about the possibility of coming back to visit myself. That would be weird, right? And it's a little disappointing that I have not in fact met myself from the future yet. It seems to not bode well for the future of time travel. But it could be that there are rules or armageddon scenarios or whatever that prevent you from talking to yourself - so sometimes when I see people I wonder if they might be me from the future, come back to take a look around.

And again some religions (religions, right?) say that all people are essentially one, or even that all reality is essentially one. That's Hinduism, right? Brahman? Anyway, if you look at things that way, then other people are really you, but just sort of a separate part of you somehow.

So how about this? What if after you die, you're reincarnated, with no memory of your previous live(s), but you're reborn without respect to time? So you could live as you, and then live as your father, and then live as your son, and then live as EVERYONE EVER. So everyone in the whole world would actually be the same entity, and if you help someone else you are helping yourself directly, because the other person is ALSO YOU.

I think I've got the makings of a pretty sweet religion here.

Quick religion check:

Can it be disproved? NO.

Check!

Does it have some advantage if it's true? YES.

(It's freaking awesome.)

Check!

Well, that's good enough for Pascal, and he was pretty smart, so if you're a betting man, come on and get on the everybody's-the-same-person religion train!

Somebody must have thought of this already, right? What's it called, I wonder?