I think you will find that there are no "formulas" for your (or any) particular rear end and transmission. There are things that others use and work for them.
I think there are a couple of threads (grin) on diff oil and changing procedures. Generally I would change to a systhetic you are comfortable with and see if it chatters. If so add a little, like in a little, friction modifier. See how that goes.
I think the reason that they all don't act the same is the way they are driven and the condition of the clutches in YOUR unit.
You basically need to read the diff threads and decide on a brand of fluid. You also need to decide on a modifier that works with that brand of fluid. Then do the change, see how it goes. Adjust, see how it goes, etc.
The only thing I can add to the diff threads is I did not raise each rear wheel off the ground so as to drain the maximum amount of old fluid to the center. I did not pick up on that. Will next time though.
Bob Weis