93yj, IMHO a limited slip differential is simply junk for offroad applications. I strongly recommend a full automatic (as in always on) type locker for the rear axle.
I personally ran several years with a Detroit Locker in the Dana 35 with 33 and 35 inch tires over some of the most difficult trails in Colorado, Utah and California before replacing the dana 35 with a 1 ton rated axle; the driverside axle tube started turning where it goes into the differential, only the traction bar held the axle tube in place. I was fortunate to have been able to get the rig off the trail and back home, a distance of about 150 miles!