I use to have the same traction limited problem in the wet with my 500SEL (Euro). I solved the problem by replacing the lousy tires (XGT V). I have since used four different models of tires with no problems with traction at all.
By the way limited slip diff will do little if your tires do not have traction. Contrary to popular believes limited slip diff is a definite aid for high speed cornering because it limits the spinning of the inside wheel and allow the outside wheel to power through the corner, thereby maintaining a high cornering speed. With an open diff power goes to the spinning wheel and the car slows until the spinning wheel regain traction. That is why limited slip diff is a definit plus for track driving. For street driving with average skill drivers open diff is a safer setup because it promote understeer in the corners. Good luck.