Absolutely run and 80w90 in the front and 75w90 in the rear. No problem. You could really run either, in both. The difference are small and akin to running a 10w-30 vs. 15w-30 engine oil. And in Tennessee, it becomes less of an issue. Climate matters, don't let that "5w-30 everywhere" Mafia cloud your judgement...
And don't be tempted to go higher on the 2nd number unless you are towing with it a fair bit. Just means more VII's to shear and make a problem.
Do check it the rear is LSD and needs additive - that's an issue. If you do in fact have an LSD rear diff, then there's another level of additive and performance-check you need to do. So verify that and ask back.
The last time I did a bunch of differentials (2 years ago?), Walmart had a full syn Valvoline 75w-90 for like $7/qt, a real steal. No Idea if it is still around in their inventory.