This noise is common to nearly all Jaguars at some point and only gets worse as time goes on.
I have 3 jags at the moment and they ALL do it.
This is a drive train problem having to do with the universal joints which connect the differential
to the whichbone assembly on each side. These "U" joints are notorious for rumbling at a particular
range of speeds, I'd say from 50-66 mph. The rumble seems to go away at higher speeds although the
increased ambient noise at the higher speeds could simply mask it at that point.
I've rotated, changed tyres, as well as replaced wheel bearings and wheels and it has never affected
or changed this sound.
Jaguar has a tool that measures low frequency vibrations as the car is in motion, it was designed for
this very type of noise detection.
I may be full of bull here, but this has been my personal experience after having owned over a dozen
Jaguar sedans from 1972 - 2001 models.
I have never gone so far as to change the universal joints, I've decided instead, to live with it.