Remathilis
Legend
They should definitely dump the real-world gods. Even the really old ones like the Sumerian gods. What I would do is make up a new pantheon or two and use them to fill up the book space that opened up when the real gods get removed.
Ironically, the Gods (or Powers, as the Cagers call them) weren't a big part of Planescape. The Greeks and Norse and all the Deities and Demigods powers are out there, but they didn't factor much into the day to day life of the setting. You could easily say "the planes are where the Powers live" and never say which powers live where. If you need examples, D&D has all the Oerth, Faerun, Krynn and Monstrous powers to use at will. You don't need to say if the Celts are out there or not.