First, the exact gear lube viscosity is not critical. 75W-90 is close enough to be 80W-90 for all intents and purposes. And for heavier uses, a heavier viscosity is recommended anyway. I run either Torco or Valvoline 85W-140 conventional gear lube in my axles.
Personally, I would not pay extra for Royal Purple despite all the hype surrounding it. And its purple color is just a marketing gimmick. That purple is just a short-lived dye added to the gear lube.
Actually, I won't run synthetic gear lubes in my TJ since several axle manufacturers determined the ring & pinion gears run hotter when lubricated with synthetic than they do conventional gear lube. The surprising discovery that synthetic does not extract heat as well as conventional gear lubes do has made a number of axle manufacturers to change their warranties to require conventional gear lubes, and void the warranty of any axle that comes back in for warranty work they found was loaded with a synthetic gear lube.
Quick question, does your rear axle have a Tracloc limited slip differential? If so, make sure any gear lube you buy says it is "compatible with limited slip differentials" on the back label which indicates it has the friction modifier additive that the Tracloc LSD requires.