My neighbor asked if I would look at his recently acquired '03 X-Type 3.0 with auto box as he was experiencing 'some sort of vibration'. Upon inspection I found that the driveshaft had been replaced with a salvage yard part...unknown year...undecipherable junkyard painted code. The alignment marks were correct so I retorqued all the bolts-44Nm-33ft/lbs. Then, off the jack stands, collected the neighbor, and out to the motorway...still vibrating-BADLY from 40-60mph...I didn't risk any faster as the dash fascia was beginning to shake. Back on the jack stands (it's getting hot by now 90+ degrees,90+% humidity)... I reinspected the driveshaft and noticed that the carrier bearing mounting bolts, though tight, were neither centered nor aligned. I refit and aligned the bearing/bolts using the tried and true 'Eyeball Method'...AGAIN, off the jack stands, collected the neighbor, and out to the motorway...very, VERY slight vibration developed around 65mph (much better than my own car)...smooth up to 85mph. Upon our return, my neighbor professed to my wife that I was a mechanical hero. With an expression that only decades of marriage can produce, she said, "I wish he would learn how to change the bag in the vacuum cleaner".
After not seeing my neighbor for about a month, he dropped by and presented me with a Diamond Jubilee Union Jack souvenir cap that he picked up while in London last week. He declared that the Jag was still behaving in a respectable manner. After the proper thank you's and pleasantries were exchanged, I told him that an ECU meltdown repair or a T/C, gearbox, engine replacement would require that I accompany him on his next London trip as payment...we laughed...I'm updating my passport.
In all seriousness, this was an EZ fix for a common problem. It may or may not work on your car but is worth the effort to give it a try. Cheers, Andy