If you don't have limited slip, you certainly don't need any additives.

I used Mobil1, but some have said (and I kind of agree) that synthetic is less valuable in non-combustion applications like differentials, transmissions and t-cases. Mobil1 in my transmission certainly made the shifting smoother.

If you go synthetic, you won't have a lot of choices with regard to viscosity. I don't think you'll find 80W90 synthetic. Even with the out of spec viscosity, the synthetics will work fine.

I'm kind of a synthetic nut--I even use synthetic grease in my wheel bearings and keep synthetic grease in my grease gun. My Trooper has been 100% synthetic for quite a while, and I'd like to think it's worth the (minor) added expense.