It sounds like you'll be alright as is. Still, I'd personally want to go with synthetic from mile one on new gears. Then just change it out fairly often, early-on
You do not want to go synthetic for the break-in. First off, you want the gears to finish the peening process. This is why gears run hot when breaking in. You'll get small flakes of metal in the oil and it's normal. The other issue is that you'll be changing the oil within 500 miles. Synthetics will make the break-in take longer and you'll be wasting the oil since it gets changed soon after. Once the break-in is done, then you can go with synthetics if you want. If you don't finish the hardening process you'll end up with soft gears and could shear them under stress.
Sure, what synth. oil manufacturer in their right mind would want you to ruin your gears from day 1
by introducing any kind of synthetic into the diff during break-in? http://www.turbobits.co.uk/acatalog/redline_lsd_friction_modifier_additive.html.
Diff additive or gear oil, they're still synthetic, just of apparently different composition and viscosity and partial or full-fill
If synth. manufacturers don't promote synth. gear oil from day 1, it does a couple of things potentially, financially positive for them a) doesn't make GM, Ford, Chrysler look like a$$holes for factory-filling their vehicles with regular gear oil b) gives synth manufacturers an opportunity to sell a "specialized" synthetic for the new gear installers out there.
Yes, you want to finish peening. You'd just want to finish peening with fewer metal wear particulates circulating, as might be created when running regular oils causing higher friction.
Keep in mind, Jeeps don't get any lighter running synthetic -- either oil, your gears are still under load "pushing the same pig." Run synthetics from Day 1 and minimize unnecessary gear wear.
