XJR Vibration woes…

[dalaifarmer]

Hi there. I bought my 2001 XJR approximately a year ago and, although I absolutely love the car, I'm trying to get to the bottom of an annoying vibration -it kind of takes the edge off an otherwise fab driving experience. Any advice very much appreciated!

It comes on at 50 mph through to around 75 mph and manifests itself as a deep rumbling vibration, as though it is caused by something with considerable mass out of balance. There is no discernible vibration felt through the steering wheel, and the vibration level does not change when the brakes are applied. It also doesn't go away if I put the transmission into neutral and let it coast. It is most noticeable when decelerating gently on smooth roads.  

I have looked across various forums and have learned that there can be many causes, most of which I believe I have addressed- namely:

New (quality) tyres fitted all round and wheels balanced properly
Prop shaft re balanced
Diff replaced for a rebuilt unit, as the old one was leaking slightly and fairly noisy.
Wheel bearings & CV joints appear don't appear to have any excessive play. 
The prop shaft UJ's and centre bearing all appear OK. 

I can only think that there must be play in the driveline somewhere, or that possibly the torque converter is out of balance - though I can't really see how that could have changed since the car was manufactured. The car is a Japanese re-import with approx 50,000 miles on the clock, I am the first UK owner. It was serviced before I bought it, but there is no other service history with the vehicle - not in English anyway! 

If there are existing threads on the forums I am happy to be pointed in the right direction. 

Many thanks in anticipation.