Haven't been on the Nest in a while(Shanebo, I haven't forgotten I owe you).
More info on the type of vibration? Speed dependent? Acceleration or braking dependent? Bumpy road dependent?Frequency(humming fast or steady thump)? Harshness(metallic or muffled)? Was it there before the u-joints were replaced, or is it new?
The pinion yoke on older Eagles does not have u-joint locating tabs like the later Eagle and Jeep D35 yokes do. If you got u-joints for the later application, they lack the circle clip that holds the cups in place in the older style yoke. Then thers's nothing but the clamping force of the straps to hold the cups in place, and nothing to center the joint in the yoke, so it will vibrate and eventually come apart, violently. You would know if you got the correct part or not, based upon whether you have the non-locating tab yoke or if the ujoint you bought had the circle clips, or if your Eagle has the later Jeep-stlye yoke with locating tabs. It would be hard to assemble the wrong part and get it centered up on the old style yoke.
If the pinion bearings are worn, the seal will be leaking more than the normal little weep of gear oil that collects crud around the seal - the area will be wet with oil. Also, you would be able to move it around by grabbing the driveshaft and pulling on it.
When you replaced the u-joints, did you possibly take the slip yoke apart(separate the two pieces of the driveshaft)? They might have gotten reassembled out of phase. The two u-joint crosses must be in exactly the same orientation(in phase), or vibration will result. In phase is where both crosses could sit on a flat surface and be in the same orientation, cup for cup. Out of phase, only one joint can sit on a flat surface, while the other one will be angled some other way.