Jag rear: shock length question

[Tom Wells]

I have a 3.8S (same as 420G) Jag rear.

Should the XKE rear shocks work, or do I need longer ones?

My present shocks are 13-1/2" eye-to-eye fully extended. When the car is lifted by the frame, the rear wheels only drop 1/2" before the shocks are extended to their maximum length.

There is about 1-5/8" of thread showing below the coil spring adjusting collar - the vendor said anything over 1" means a stiffer spring is needed.
The present springs are marked as 350# springs.

There are four coil-over units.

I think I need a longer shock - say 15".

Any expertise out there?

Tom

PS: This probably explains the handling problems where the rear "skips" sideways under spirited cornering on the racetrack, and also the "bobbing" or "pitching" when the car goes over bumps at speed - sometimes it bounces me 2" clear of the seat!