When Rumble comes out it would be really cool if it had online multiplayer (It might already, I'm not sure) and someone could make an EGGNOGG world championship to see who the best players are.
EDIT: For now you could use something like Parsec I guess.
Well, If you're going on deaths or rooms pushed back I think it should be whoever is losing (closest to their NOGG) that gets the sword. I do think it's better to just give neither a sword though.