Here's an interesting issue:

Under hard acceleration, the car pulls like a train, but between 4k and 5k rpm the revs climb faster and between 5k and 6k it feels like I suddenly gained an extra 50 Horsepower and the tires get a little squirelly.

I have been able to recreate this in first and second gear. I have no warning messages. It almost feels as if a big turbo spooled at 4k and came on boost at 5k rpm or like if VTEC suddenly hit. But throughout it all, I can audibly hear the supercharger spinning normally.

The result is that the acceleration feels dramatic and the powerband does not feel entirely linear.

 

Powerbands are never entirely linear against revs and, of course, the higher the revs the more power is produced up to a certain point, even in a supercharged engine, so I suspect your Jag is behaving normally.

Richard