I'd check the u-joints for slop, had the same exact symptoms on mine and it ended up being a VERY worn out U-joint. When you let off the gas, it releases the tension in the u-joints, and that keeps the vibration from being transferred into the chassis.
But you can't just crawl underneath and check. You have to chock the rear wheels, release the parking brake and make sure the truck is in neutral. Otherwise, since the parking brake is mounted on the back of the transfer case, the truck will roll back and put tension on the driveshaft that will make you think that everything is solid.
My oil line fix
My 100k stopped odometer fix
Brace for impact, I'm in a "modifying mood". Massive thread count inbound.