Sounds like a good case for a new 5sp conversion. Think the 2.88 will make you suffer until you get some RPMs. So in the hills if you miss a shift, you are done.
What, the XKE is already a a 7 sec.+ car with a 3:54? Even a 3:08 will be a major drop.
If you have to keep the 4 sp. you might consider the 3:08 and two sets of tires and wheels depending on where you are driving. Taller or shorter tires will also change your ratio. I know, that can be expensive unless you already have extra wheels.
Good luck
Mike