Informative thread thanks, you mentioned knocking the caps off the u joint when working on the differential. It's been my experience that 1 or more of the needle bearings will often lay flat inside the cap if the u joint has more than a couple years of wear especially if it's a warm day causing a vibration whenever under load.Evidently I never updated this. I ended up swapping the 6° out with a 4° shim one day in 2021 after Dad said the problem was still there, if not worse.
He said the 4° helped it a ton, but it still wasn't 100%. I got to thinking though, and I'm not sure the trans mount has ever been replaced. That may be the source of the shake.. but we'll see. The car is going in for trans work and Pops is going to ask the guy to verify all of that.
Good luck!