I replaced 2 out of the 3 U-joints in the main drive shaft (I boogered up a bearing cap on the 3rd new joint, gotta get another one). It made quite a difference. The old joints were definitely bad - there were grooves worn into the machined ends where the needle bearings ride. But there was no easy way to tell that without actually removing the old joints - they all felt fine when manipulating them by hand with the driveshaft on the ground.
The truck still shakes at certain speeds on the highway, but I think I have that narrowed down to a bad slip yoke bushing in the transfer case extension housing. See here:
https://www.cumminsforum.com/threads/vibrations-around-65-70mph.2258009/
Will report back once I get that replaced.