I never understood why these electronically controlled differentials still needed the friction modifiers. I hated that whole mess with the mechanically engaged differentials. I thought the whole point of an electronic diff was to do away with that mess.
Adding an abrasive to synthetic oil, yeah that makes a whole lot of sense.
If it does need friction modifiers, change the oil often and skip the synthetic. It turns to mud.
My old Audi had 2 manual electronic locking diffs and I don't think it needed friction modifiers.
You could probably use this stuff