Rear diff fluid and friction modifier?

Hi. I am about to change my Rear Diff fluid. My rearend is the Corporate 8.25 with a trac - lock limited slip. My Question is if I change to synthetic fluid that states it is for limited slip applications do I still need to add friction modifier or is it already in the fluid? Will putting synthetic fluid in with residual regular fluid harm anything? What is the best way to clean out the old fluid? I was thinking Mobil 1 synthetic fluid. Is this good or should I get Mopar? What about friction modifier. Is Jeep the only place I can get this stuff? Should I just buy mopar original fluids (non-synthetic) with friction modifier made by Mopar to keep things simple?

I use Mobil 1 (availability) and you should add the MOPAR friction modifier (it seems to work better than the Generic stuff at auto parts places)