There are a LOT of oils out there now but all you need is very simply a bottle of GM posi additive and a quality 90 wt or 85-140 non synthetic gear oil. I use Lucas 85-140 in all my diff builts with the bottle of Gm additive. I coat each clutch in it while assembling but since I custom tune the posi without the springs I never need more then one bottle per oil change and NEVER had any posi hammering with any of them.
With a stock spring loaded Eaton or new Loaded Eaton with those crappy fiber clutches and Heavy springs you may need 2 bottles. All depends on how the posi was setup, which with production built units can be all over the place.
Suck out as much of the old stuff,(do it hot) and then add the new oils and do figure 8's and see how it it.