Sorry, I have to disagree with you gentlemen on that. Tire vibration will occur whether on the gas or not. The problem is somewhere in your driveline.
Have you changed the rear end gears? Improper setup will cause vibration on the coast side of the gear but may not on the drive side. It will eventually shear the teeth off.
Also, the u-joints may be worn out. Get under there with it in park and twist the driveshaft to see if there is anything unusual in the u-joint dept.
You already said your t-case was shot. The transmission drives the t-case, so all power is transmittd though it. Could be bad bearings there.
More than likely it is in the driveshaft or u-joints. When you stay on the gas all the slop is taken out of the drivetrain. When you let off, it tries to coast or idle, spinning without any power transmitted and the slop shows up again.
I had the same problem in my 97 Burb. Turned out to be the u-joint at the pinion yoke.