Just wondering if the pinion dog bone has been removed. Could this be an easy solution for the vibration? I wonder....
Also, how may ppl out there actually have their drive shafts balanced after a U-joint replacement? How many shops (short of an all out race shop) actually have the equipment to balance a drive shaft?
Heck even the Ford service manual doesn't have a step "balance drive shaft" under U-joint replacement.
Question? How long has it been since your rear differential has been serviced? How hard are you on it?
From my personal experience I have had a number of issues with the service life from Ford 8.8 rear ends. I don't race and I don't abuse it (well not too much). I do perform more frequent service than Ford recommends. Yet both of my Mustangs have rebuilt rear ends (80k and 145K miles).
If this were my car would put it on axle stands and run at idle. If the car has traction control, disable it. This will also make the dash warning light come on. Don't worry about it. It will clear on it own after a short while of normal driving.
Use a mechanic’s stethoscope and probe around the differential housing near the pinion. Listen for the roar of bad bearings. Next carefully probe around each axle tube. Again listening for the roar of bad bearings.
Consider inspecting the rear diff gear oil. Examine the sump for metal. For a serious inspection, pull the half shafts and carrier. Inspect the load bearing surfaces of the half shaft. If not smooth, replace. Inspect the carrier bearing race surfaces. They should be mirror smooth.
If the half shafts are damaged, it is possible to get a "service replacement" wheel bearings. The service replacement relocate the bearings outboard of the factory location. This may allow a worn half to be saved thus saving $$.
If no problem found, disconnect the drive shaft and check the pinion for excessive in/out up/down play. If done while the carrier has been removed, it is possible to get a better "feel" of the pinion bearing's condition.
The pinion bearings are much tougher to replace. Wheel bearings and carrier bearings are much easier.
Checking motor mounts and transmission mounts have already been mentioned. Don't forget, if the factory mounts have been replaced with after market units, sometimes more NVH should be an expected result. After all, there's no free lunch.
There is a procedure in the Ford service manual to isolate suspected drive shaft imbalance. It involves using hose clamps installed around the DS. The clamps are rotated in a pattern to try and determine the best balance point. It's a detailed labor intensive trial and error process. Taking good notes is important to get better results.
The importance of tires, shocks, and bushings should not be overlooked as possible vibration sources.
For drive line NVH issues it can be a real PIA to track down. Sometimes taking the car's history into consideration can help narrow down the possible sources. Again, there often is no "easy" answer.