What to do about a useless limited slip rear end?

FWIW the front end being heavy does not make the rear end light. The PSD simply makes more power at idle than the gas equivlant and that effects traction. It doesn't matter if the front weighs 3000 or 10000, if there is 4000 on the rear end it is 4000lbs.

Your average diesel also weighs more than 450lbs more than its gas counterpart...thou you did not specidy what year you are talking about.