Sounds like you need to replace your diff fluid. The new LS diff fluid does not require additional friction modifier. Takes around two quarts, but purchase three so you have enough to get two in there.
Then go do around ten figure eights to get the fluid in the clutch packs.
While you are at it, check your axle nuts to make sure they are tight.
If not you can torque them to 130 ft-lbs for now, but best to get new style axle nuts which require 160 ft-lbs of torque and 272 lock-tite.