This is kinda long shot, but related to 4Crawler's point - I wonder if you are having axle wrap problems. Could'has anything torqued your rear end lateley?
e.g. maybe after so many years, a spring is simply failing/warping, but only under load. That woudl cause the pinion angle to be off, but only when accelerating.
Heck could even be a loose bolt somewere in the suspension?

here's an idea (nice and dangerous too!)
Jack it up so the rear is in the air and very well supported. Have a buddy watch the driveline while you apply the gas, watch the speedo and see if you still get the vibes like that. They maye be able to see how much movement there is.
9when I did this recently I tied the rear bumper to a tree for safety ;-) )