Re: 3 Registries for the Yamato?
Renaming would explain away that one, though: the already fully operational USS Risk Investment, NCC-71807, could have been renamed Yamato to honor the lost ship.
I don't quite buy that explanation either. Why would it have been so important to quickly rename another ship Yamato right after the first ship was destroyed? It's not like she was such a noteworthy ship or anything.
I never make mistrakes.