Never mind: a search found my answer

https://www.jaguarforums.com/forum/x...manual-107758/

I thought I had looked before. Oh well.

 

When I buy a car I always add a bottle of injector cleaner to a half tank of gas a couple times and it seems to smooth out the idle.

 

After all my digging, the answer was far more simple than expected.

When I inspected the ignition system I wasn't a thorough as I thought. By accident I popped the distributor cap off and found corrosion on all the points. After that was cleaned off the car ran significantly better...

*sigh* This is what happens when I don't cover all my bases. I thought this step was covered already since it was only certain RPMs that gave a running problem.

I've always made a habit to always inspect everything in the ignition system when I purchase a new (to me) vehicle. I must be growing lazy or something.