I have a 1982 6 cylinder cj-5. When it is in 4 low, and under stress, the stick shift will vibrate violently-enought that it has disengaged twice. In addition, it has sheared the universal joint twice. I have replaced motor mounts, and transmission mounts. Could it be a bent drive shaft, rear axle alingment, transmission linkage....
Which joint has gone bad twice? The problem is probably in that driveshaft. In low range, the balance of the drive train components isn't going to enter into it. Alignment of the differentials and transfer case could be the culprit. It would be helpful if we knew more about the drivetrain. That's a hint - read the first post on the board, and then put some more information in your profile.
If the driveshafts have cardan U-joints, the pinion shaft should be approximately parallel with the output shaft of the transfer case, and the joints must be in phase with each other. If there is a CV joint at the transfer case, the pinion shaft should be pointing approximately at the CV joint. Any other arrangement will cause a cyclic vibration in the power transmission through the shaft that will get transferred into the transmission and can cause problems if it's bad enough.
Your post says that the vibration is worse under load. That suggests a bad U-Joint that is allowing the alignment to get worse under load. Or it could be that the load is squeezing all of the slack and cushion out of the drivetrain and causing the vibrations to be transmitted into the transmission. Are you sure that all the joints are in good condition?