I'm not sure this is the correct place, but here goes!
I'm J. Burnett, 73 yrs young, and have worked on Jags since 1954 (XK 120).
Worked on the third XK-E imported into Canada (Norm Namero crashed the second one racing, against factory advice, and the factory bought ours back after a year since the warranty work had far exceeded the purchase price of $6100)!
Currently running 2002 XJ8 base, 38,000 mi, 2003 XK8 base, 23,000 mi, 1998 Audi A4 Quattro, 235,000 mi, 1999 Audi A6 Avant Quattro, 176,000 mi (both are 2.8 V6), 2006 Miata 6 speed, 60,000 mi, lastly a 2002 Dodge 1500 pickup 4.7 liter 5 speed.
If I may, I'd like to post a question regarding the XK8. I purchased this car with 19,000 miles on it. The tires were only 1/2 worn but were well past 6 years old and vibrated. A set of Yokohama YK 580 vibrated badly even after road force balancing (two of them could not be reduced below 26 lbs.). Have just mounted a set of Michelin Pilots and the vibration is much less. There is no dynamic or static vibration at any speed but the whole car will tremble, wax and wane, not in phase with wheel speed or drive-line speed. I'm suspecting secondary vibration set up in the rear sub-frame possibly due to deteriorated sub-frame mounts. Has anyone encountered such a problem and fixed the cause?

 

Not sure from your description, but try clocking the driveshaft at the rear joint to a different orientation in case the joint was parted for some work. You must know that the jurid coupling is only allowed to be separated on the differential flange side.

You can also try the center joint ... loosen the hanger ... spin the driveshaft to line up the hanger+bearing ... retighten wherever it happens to center.

Maybe the grease is just dried up in the u-joints with only 19k on a 2003.

The next thing you want to do is make a few posts so that downloads are available to you, then download at least JTIS and JEPC.