Here is an idea that I came up with in a flash last night. It's a tournement format for backgammon, called "Duplicate Backgammon". It is similar in concept to Duplicate Bridge, where all teams play the same cards.
It would work like a double RR, but each game has the same rolls, but with each player playing different colors, hence, the rolls are "opposite". This would add much more skill to the game, as a player must play both sides of a rollout simultaneously.
Of course, some precautions would have to be taken to prevent a player from "looking ahead" in the rollout, but hiding the next roll until both games have moved should be relatively simple to program.