Several months ago I had the same issue with mine, and it actually ended up being 2 items.
The first was my rear transmission mount, not the actual mount, but rather the transmission mount mounting plate and the bolts that are threaded into the transfer case. These required oversizing with new threads as the originals had been stripped out.
The 2nd issue manifested in losing 5th gear, but prior to that I constantly had the feeling that under firm acceleration in any gear, that something was moving or shifting sideways.
After replacing the fifth gear and installing and correctly torquing the upgraded nut (which I stake welded as well) the truck is tight and has no issues.
One thing that I really noticed as a difference is the amount of movement that the shifter had prior to the fifth gear failure when transitioning from no (or very little) load to full load. A small amount of excess play in the mainshaft translates to a large amount of movement at the shifter knob.
After the repairs to the fifth gear, there is considerably less torque deflection of the shifter knob when transitioning between little load and heavy load (a. k. a. throttle).
HP