I would guess it's the diff pinions rather than the Ring and Pinion. I don't know what these were equipped with but some other vehicles in this time period had diff pinions that were net formed (rolled to shape) rather than cut. They were softer and could deform when loaded aggressively. That only gets worse as the lash is increased. I agree with the earlier comment that if the primary drive gears were grossly out of position they would get noisy.