Wow. I have no interest in this game at all. Sorry Fencer (et.al.) Other than being played on the same board, this game bears no resemblance to backgammon at all.
I think LionsLair has a great idea for a variant. (I don't think you should limit doubles though). This would make for an interesting game. I think that instead of limiting doubles you could do something else to benefit your opponent when you choose to play doubles. (Perhaps your opponent would automatically get a doubles option on the remaining dice).
1) A mix between Tabula gammon and Russian Gammon. Basically like "race", all pieces start off the board - BOTH players race the same direction around the board, bring in their pieces in the same area - can only move their pieces 1/2 way around the board until all of their pieces have entered the board - 2 dice only - no special double rules - rest of the rules like current gammon/race rules.
2) Domino-Gammon - I have since seen some other versions talked about, but linked are the rules that I have made up for the game.