What Differential Do You Have in Your 1965 Barracuda?

The 8 3/4” was available by late 1965, although always as an extra cost option. Mopars big fix for the weakness was to make the 7 1/4” Suregrip standard on the 4bbl cars. I would bet that under warranty, the 8 3/4” was not the first repair, it was probably given to repeat “offenders”, after a couple times into the dealership.
My 65 Barracuda, which I've owned since August of 68 when it had 35,000 miles on it, was originally a Commando 273 4 speed. It had a 3.23 open 7 1/4 rear (no sure grip).

The original 7 1/4 rear lasted 90,000 miles (long out of warranty). Replaced it with a junkyard 7 1/4 that lasted 20-30,000 miles. Replaced that with an 8 3/4, some time in the early seventies.