Thanks for the pictures and info. A nice looking car!
If the car is sitting at level ride height, the pinion angle, being a "welded-in" at the factory situation, should be fine or "within specs". Once assembled and it got as far as it apparently has, it doesn't change. Most "shake on acceleration" issues arise when the vehicle has some load in the trunk or rear seat, not just driving around, from what I've seen. But even then, certainly NOT normal within the arc which the rear u-joint makes during top-to-bottom vertical rear wheel travel.
But "something" had to have made the rear springs sag as they apparently did. Like towing a light trailer or heavy items that were in the trunk for extended periods of time. Both my '70 Monaco Brougham and '80 Newport have sagged rear springs. The '70 had been used to haul a travel trailer around for a good while. When I got it, it had rear load levelers on it, and it STILL sagged until I replaced them with Gabriel Hi-Jackers, which have worked well for me. The '80 had been owned by an oil field tools rep and had a angle-iron trailer hitch on it, with Midas-brand air shocks. With no pressure in them, the rear end was too low. So a new set of Monroe air shocks fixed that nicely. The air shocks were and still ARE a band-aid fix, but all of that was done before I knew of ESPO and such. But as it's all working well for me, I'll keep things as they are. The '70 is a 383 "N" car with no trailer package, but the '80 has the "load carrying" HD suspension (no rear sway bar) from the factory.
Barring any significant body re-alignment with respect to the spring mounts and front structure mounts, which should be obvious on a lift, that leaves the only OTHER spinning item under there. The driveshaft. As a noise control strategy, some manufacturers have used various dampening methods for their tubes. One is the varied-diameter tube. In some, when cut open, there's a thin piece of soft cardboard inside of the inner circumference. Others have used rubber donuts inserted into them. If some of that stuff has deteriorated, they can move around internally, which can cause some unbalanced situations. As they can now move around, the vibrations might change between driving cycles, possibly. All of this has nothing to do with how "straight" the tube might be.
The issue of the cracked trans pan gaskets is interesting. Unless some very substandard rubberized cork gaskets were used (not OEM-spec, or similar), the only thing that might make them brittle and hard is heat. They can't dry out as when the engine stops, the torque converter partially drains into the pan, and the fluid level can get higher than the neutral safety switch on the side of the case. No way the gasket would ever "dry out" from sitting, that I can see, with the trans oil level being that high when the engine stops and sits overnight, stopped.
"Road force balance" is a tire/wheel balancing technique which more new balancers incorporate, especially at the dealership level of things. Once the wheel is mounted to the balancer, a fixed tube is rolled against the tread as the balancer slowly spins the wheel/tire assembly. Then the balancer will spin it faster, sometimes, then give the readout of "road force variation" as it also indicates where the balance weights should be. No "splitting weights" with these electronic balancers. The road force variation amount is also displayed. Sometimes, you can reposition the tire on the wheel to minimize it, which I believe happens BEFORE the wheel assy is spun for the weight applications. Goodyear calls it "ride variation", or something similar, not embracing the "road force variation" terminology that the OEMs typically use. I think that in the "old days", such road force variations were termed "hard spots" where the tire carcass is put together and the plies overlap?
With the rear axle safely supported on jack stands, slowly turn the rear wheels and look for wheel lateral run-out, which could be an axle shaft flange situation in addition to a separate wheel issue. Is the vibration there with the wheel covers off the car? Just curious, considering how heavy those are in comparison to the standard Cordoba wheel covers of those years.
Does the rear trans crossmember show any evidence of being deformed? What about the rear trans mount? The only other place where driveshaft angularity can be altered.
Just some thought,
CBODY67