<Luck is definitely a factor in the backgammon ratings but it is not *the* factor. As many said, the real factor is that with the same skill difference as in chess, the better player win percentage is a lot lower. But this has to do not only with luck, but also with the length of the game. For example, if the game of go was played here with the same rating system, you would soon see people over 3000, because in go you almost never win against a stronger opponent (while it still happens in chess).
The solutions could be :
1) Implement and play only "Pro backgammon", matches to e.g. 5 points with a doubling cube, which is a much better game anyway. But implementing that would probably be a lot of work for Fencer.
2) Tuning the Elo formula. In the Elo formula there is a constant of 400 which means that it requires a rating difference of 400 points to have a winning expectation of 10/11=90.9%. Changing the 400 to e.g. 600 would dilate the rating scale so that you are 600 points higher than your opponent instead of 400 when you win 90.9% of the games. But this is not a so great solution as it looks, because it requires for each game to estimate the relation "skill difference -> winning expectation", which can be done only in a somewhat arbitrary way as the "skill difference" is a subjective value.
3) Accept that because of the nature of one-game backgammon the rating scale will always be shrinked and that the rating differences must be taken as meaning a higher skill difference than you would expect !