I have interest in running Diablo 3: Reaper of Souls on Xbox One. There are existing categories but for PC. I think that because of game and load time differences that the Xbox/ps4 categories should be separate. Should I request an entirely new game or contact the Mods requesting new categories?

Imo you should contact the Mods, because if you just request that as a new game it will probably just create confusion between runners.