If I use an existing universe for an RP it tends to be set in an alternative timeline so I still have free reign of everything.
This. I feel that if one follows this sort of thinking that things just tend to work better. It's what was done for the One Piece RP and sort of what I'm doing for the Unova RP.
I definitely feel weird if an RP is set in a universe where canon characters are present.
Actually, I think I'm generally put off by RPs that are set in universes too similar to whatever they were based off of, with a similar plotline. I can absolutely see the appeal to them, but they're not really for me. Even in terms of Pokemon, I've always entered RPs that have a unique spin to them in some way.
Friends for Infinity
art (right) by the amazing Kitty