Fencer: I agree, since it would be a very different game.

While I'm in a creative mood, I thought of another variant that I call hybridgammon. The game would be played in sets of two matches with the players taking opposite colors; assuming the colors are black and white, then white always sets up in the backgammon position, while black sets up in the nackgammon position. Thus in each set each player will start one game in the nack position and one in the back position. Black always rolls first.

Another way to approach it would be to play, say, 7 point matches, with the players alternating starting positions. Again, black (nack) would roll first.

The player who starts in the backgammon setup would have a slight advantage in each game, so it's necessary to do something to balance the advantage.