This is a very old, very long sci-fi fic that I think I remember was completed.

Kagome, Kikyo, and Kaede were sisters whose world was being overrun with I-forgot-what. They were rushed into cryogenic pods and when Kagome wakes up hundreds(thousands?) of years later, hers was the only one not destroyed by time or debris.
She wakes in a futuristic world where people go to academy and train to ride dragons(at some point they go into space and travel to Jupiter or something.) She encounters reincarnations of her sisters in this world and has to deal with that. At some point towards the end, they battle the big bad Naraku.
I should point out that I'm fairly sure that this was a Kagome/Inuyasha fic, so it's not really relevant to this site, but it's been tickling my brain on and off for ages now and I thought I'd throw it up and see if anyone recognizes this. Thank you for your help!