The '62-'67 Chevy II's never came with an 8.5" rear. Just the old drop-out 10-bolt and, later, the newer integral 10-bolt. Later high-performance ones had the 12-bolt, but those are quite rare.
The '64-'67 rear might work, and is the same 8.2" unit used in their bigger cars, just narrower. It can handle a mild 350 if you don't beat on it real hard, like side-stepping the clutch with slicks, etc. It does require 5-lug wheels, though.
I'd keep what's in it, and just don't be too rough with it. If it gives up the ghost, try a later unit, or have an 8.5" one narrowed to fit.