Fair play for being honest, most people don't.
It's hard to go from a sports coupe to a GT, and you do need to adjust your brain and expectations a bit. There are ways of making the car what you want, but at what cost? I reckon the Jag could be made to be better, but you'll never get round the weight and size of the damn thing.
Depends how much more you're happy to put in, and whether you think you'll get that value back in enjoyment. I'd definitely start by changing the stuff that's easy to do (fit softer padding to the arm rest, remove some sound deadening) but after that I don't know. I had to do a fair amount to mine to get it to handle rather than waft, would you be prepared to do the same?
As obvious as it sounds, especially coming from me, but a 911 would give you the best of all worlds. Chuckable, waftable, involving, and a decent size fuel tank. But it's not a V8, and the pull of those is strong!