I'm really starting to get dissatisfied with the help on Stangnet, I've been posting and helping people on here for years but it seems when I ask a question that isn't about mufflers or CAI, people have no clue or don't want to help.
The resident Stangnet rear axle expert is on vacation this week. Or was he the guy that won the big lottery and bought a new Lambo?
Seriously, this is a community where a lot of people come and go, and someone that has a setup exactly like yours may not be online at this time.
Check the simple stuff first:
Does the Auburn Pro diff use the same lubricant as the trac lock on the stock Mustang 8.8? If so, did you add the friction modifier. If not, did you use the correct lubricant for the Auburn Pro and the right amount of it?
Check the lubricant level using the pinky gauge. Yes, I know gear oil stinks and your pinky will smell bad for a week. You are probably thinking that's a dumb statement, but do it anyway.
Did you lube up the axle ends, bearings and seals when you put the axles back in? They should have all gotten a coat of lubricant.
Did you inspect the axle shaft bearing areas for dirt, scratches or damage?
The cross pin, C clip parts and spider gears should have also have gotten a good coat of lube.
Did you put the thrust washers back in behind the spider gears? Did you lube them up too? It is easy for one of them to slide out of place when the spider gears are removed and installed.