8.75 binds

I think I came across this once with a loose pinion nut. When the D/S drove the pinion it was ok, but when the ring gear drove the pinion it pulled the pinion into the case and jerked the car. I seem to remember one way was worse than the other.Long time ago,lol

I was going to mention that it sounds like when a pinion is loose.
That can do damage quick, so grab the driveline just up from the ujoints and see if the yoke on the rearend moves up/down or sideways at ALL. (with the weight off the tires)
If it does, that is what's causing the binding.