You are correct that Kharne is incredibly good in team games, to the point that every team game has to specifically play around him both in how they construct their books and how they play. And there isn't really much you can do if they time the summoning/attack correctly with regards to initiative, like you said.
I could see a houserule for team games that limits Kharne to only getting melee +1 for each enemy creature that ONE of his opponent's has. That way he benefits from whichever opponent has the most creatures at any given time, but won't ever be anything more to worry about than he is in 1v1 games. No matter how big the teams or FFA match is.