I'd not be content with the "head gone soft" report. it bothers me.

 

If a head has come from a USA car it will definitely be lower compression. Also, your engine is an HE, so beware being supplied with a pre HE "flathead" head, which will NOT work at all.


It is worth contacting the people who placed this advert:
NEW JAGUAR 5.3 V12 XJS V12 ENGINE AUXILIARY SHAFT C38421 | eBay


or these
Home - potteriesjaguarspares.com


I have only dealt with the first link who were very decent guys. Like others, I am a bit sceptical about "heads gone soft". Why not ask them to explain further and take some snaps and post the pics and explanation on here?
Greg

 

aluminium heads do go soft if subjected to excessive heat. An engine rebuild shop can test them using a tester made for the purpose.
Cylinder Head Hardness | Southside Cylinder Heads, Engine Reconditioning Australia
The shop I use attaches indicators to one of the welsh plugs on each head they rebuild which deform in some way if overheated. (these are for the purpose of determining warranty liability)