That's kind of a dangerous blanket statement there.
Shackles, in and of themselves don't make vibrations.
What I suspect you've done is to rotate the pinion up. This will make the lower u-joint operating angle different than the upper u-joint operating angle. Normally, these phase-cancel each other out because they're the same. When they're different, you get vibes because one u-joint isn't fulling cancelling out the rotational speed differences created by the other.
Okay..... that's probably clear as mud.
Take a single u-joint, and keep the input shaft and output shaft parallel. If you turn the input shaft at a constant speed, the output shaft will also turn at the same constant speed. Now, keep the input turning. Move the output shaft so that it starts to put an angle on the u-joint. The output speed will no longer be constant, but will vary slightly above and below the input shaft speed in a sine wave related to the angle of operation. This is a vibration.
Add a second u-joint at the end of the output shaft so you now have an input shaft, u-joint, intermediate shaft, u-joint, output shaft. The u-joints do need to be phased, and for the moment, I don't remember what the phasing is (hint: look at a stock rear driveshaft for an XJ.) In any event, as long as the output shaft is parallel to the input shaft, you'll get smooth power transmission. You'll get a sine wave in the output speed when the input and output shafts aren't parallel. Again, vibration.
Back to your situation........you've lowered the operating angle (made it closer to parallel) at the axle u-joint, while the tcase u-joint hasn't changed. Possible fixes? Lose the Chevy shackles, put a reversed degree shim under the springs, or put in an SYE kit (which will probably also require degree shims.)