I ran plain 70-90 gear oil. No synthetic, no friction modifier.
Same as i did in my mustang back in the day. We would add the FRPP clutch packs and skip the modifier. All the friction modifier does is make the fluid "slippery" and allow the clutches to slip easier. Some people report issues of the clutches chattering but I never had an issue with it.
Depending on your pinion angle and diff cover, you'll need to adjust the amount to cover your gears and lubricate the pinion. Some fill it to the brim. I fill it through the abs hole at the top til it comes out the front hole and then plug it off and give it a little more.
I wouldn't use the expensive stuff in the diff if you're gonna break in the gears and clutch packs. Or if you're like me and have water crossings that cover the front differential.
Typically an LSD uses a friction modifier. The instructions that came with the Ford Racing LSD specifically stated to use non synthetic with a modifier. You can buy oil with or without it. You add the minimum at first and adjust based on how much chatter you get around corners.
I had a couple of bottles of Red Line's modifier left over from the race car so I bought 4 qts of NAPA 80W-? and added it per the instructions. There's a little chatter around sharp corners so it should be just right.