I think I have traced my intermittent problem with feeling like I am driving on bricks to it does it when the battery is low. In fact, I think the lower the battery, the worse the vibration. You can actually see it in the wheel. When it does it, it is consistent across the RPM range and at all speeds.

Is there anything that would cause this to happen with a low battery? This is not an alignment or balance issue.

 

May be causing misfires. Presumably not bad enough to flag codes.

These cars cannot stand a low battery.

 

I'm not exactly sure, but around 2014 Jaguar changed the steering rack on the XJs to an electrically assisted power steering rack. The only exception was the XJR for a couple of years remained hydraulically assisted power steering, but it to is now electrically powered.