Hi I not long had my first xj40 and it seems that there are some similar problems.
I've not cured them at the moment but I'm investigating, and this is what I've found:
Firstly the howling noise, mine is definitely connected to the diff as I've had the car running on stands in the garage (a little nerve wracking) and listened to the rear end whist in D. Prodding the throttle reproduced the howl momentarily (which was loud in the confines of a garage). I'm intending to replace the bearings first in a bid to fix this prob, but I'm not convinced as the howl sounds gear related and there is oil leaking from all the in/outputs, suggesting that it may have covered many miles low on oil (it was a reps car and covered 65k in 2.5 years!). The main difference between my noise and yours is that mine makes the howling noise (amongst other more subtle noises) at any road speed, most notably around town at light throttle when the cabin is quietest. Could be the same/similar thing? I'm not sure...
On to the vibration. It is interesting that you should say it occurs at
50mph as this is about the point (out of sport mode of course) that the gearbox changes to overdrive 5th and locks out the torque converter (this gives better cruising mpg as there's no power lost though the auto box). The gear change is very smooth, or course, and easily missed (check the rev counter as you approach 50). I have noted this is the exact time I get my vibration, which also lessons to a small extent the faster I drive. I've also felt the vibration through the seat/transmission tunnel and steering wheel at the same instant, suggesting to me a large mass is moving around, enough to enable its effect to be felt through the wheels.
During my fiddling under the car I grabbed the gearbox tail and heaved it around, noting that it moved around easily (once you get over the inertia of the thing) up to about 3/4 of an inch from center. I know there is a spring based mount located here and that they are prone to collapse after a while. I'm not sure what its supposed to feel like? Anyone?
Could it be that when the box changes up we are experiencing a low rev high torque situation, just enough to cause the whole drivetrain to wiggle about off centre?
Hope this has given you some food for thought?
If there is any one out there who works on these cars regularly, surely you've come across this before?
Best regards
Mr Smooth