This stuff I'm using is Lucas white lithium grease. Any kind of tacky multi-purpose grease would be fine for the pinion and ring. You don't want something too light because it'll fling off, if you go to heavy you'll have some unneeded resistance. I like marine greases the best. Special lube 101, 2-4-C or Quicksilver extreme is really good stuff. That said I don't think you need to spend big money on grease for differentials.

Can you be more specific? Are you talking about the output shafts from the differentials or the drive cups? Do you have movement of the entire diff in the bulkhead housing?

Very little movement but yes, very very small movement but yes, they do swivel side to side a very very small space in between pots so pots don’t warp or strip or wear the against the plastic small, but limited spacing

I'm still a little bit lost on exactly what component we're talking about. Can you help?