64 cuda original rear end

NAPA has a GL-5 API Service rated gear oil 80W-85W-90 that is for limited slip differentials. They also sell a "friction modifier" that is intended for limited slip differentials.

I used both together in my 65 Dart 7 1/4 suregrip differential after rebuilding it with new bearings & seals & adjusting/tightening the pinion/ring gear backlash to specs by replacing the spacers.

I'd recommend you pull the cover, clean things up, & check the backlash before investing in the fluids.

Is your pinion seal leaking?.....another item to fix before investing in fluids.