I had severe vibrations at anything above 40mph, only under load.

You'll want to replace your rear subframe mounts, that helped me considerably. My next step (since I still have them, just not nearly as bad) is the center support bearing for the driveshaft. If your subframe has been moving around (likely the mounts are shot due to age) then your diff has been moving around and putting strain on the center support.

The rear subframe mounts are at the four extreme corners of the subframe (diff carriage) look for four large mounts which bolt up into the chassis behind the rear wheels (if looking at the side of the car straight on)