I just finished an experiment related to vibe and shake. Installed leaf spring clamps about 4-5" behind the rear axle. Huge reduction in both.. Not perfect but 80% better... My tires are road force balanced perfect (I had a severe shake due to RF balance but that's fixed).. I think the rear axle is moving around causing the shake/vibe to transmitting up the drive shaft, through the transmission to the engine. Engine shake is shaking and grounding out the motor mounts but the source is the rear end. I suspect one of three problems.. 1- crap leaf springs, 2- ring/pinion, and motor mount ground out (needs 3mm shims)
My idea came from the fact that my truck rode better after I had it parked facing downhill or it changed based upon weight in the bed. Noticed the leaf spring spacing looked different every other day.. Floppy leaf springs are causing the rear axle to float around and then the drive shaft oscillates.
Next steps - traction bars from calvert racing or replacement leaf springs... Check ring and pinion backlash..... Either new motor mounts or 3mm shims... Most likely all three of these items need to be done for a comprehensive solution.
It's been a year and I'm done with GM.. fixing it myself.