A four pound cap would be my choice as well. A 13 or 15 pound one seems like a recipe for leaks.
I am going by it’s a XJ6 Engine , I hope there will be leaks , leak’s into the Expansion tank 
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The altitude issue re the 13 / 15Ib cap is, no doubt, a consideration, but more likely a reason is that later XJs are fitted with 84 / 85 degree thermostats, so with an engine at that temp you park up after a vigorous ride, coupled with a high ambient temp, then heat soak elevates the temp upto and above 100 C. Now with a low pressure cap this probably results in a pool of water under the rad and the engine gurgling merrily away when you return to your vehicle 10 / 15 mins later.
No matter which engine ,XK type that is,
I would not fit a thermostat above 70 / 74 degrees , with the rad cap at 4 / 7 Ib
Opinions differ, but to aid longevity and less hassle, I prefer to maintain a running temp in the 70 / 75 degree range. The higher temps on the later engines all to aid emission requirements
of course. Modern engines running high temps designed to do so.
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I used a 13 pound cap on Tweety, and it had had such most of its driving life: no leaks.
It was utilized when he was a race car, with its massive NASCAR radiator.
What for? what temp, depending on ambient, did the engine run at?
On the track, sustained temps of 220F were not uncommon, and in traffic, it kept “burps” to a bare minimum.
Well yes ! 13Ib cap running @ 220F !!
As you state, re rear main seal etc, operations you have carried out many times, as yours truly, in your case though, in running @ 220F were these operations carried out on the same engine?
Each pound of increased pressure raises the boiling point of water by 3 degrees. With a 50/50 mix, that gives you a boiling point of 265 degrees with a 15lb cap, vs versus around 235 degrees with a 5lb. I run a weak cap on old cooling systems that I don’t trust, but 15 lb on anything else.
First long run in the Jag today , as we are still in lock down , after fitting Expansion tank , nice to see water in the filler neck , about 10mm down from the cap , a first for me 
Hi Brian Re a post you made some time ago re 340 Jag with 3.8 engine. Can I contact you to discuss please?
Sure I guess you may have a “380” if so what is your problem
I looked up my list and I think you have EE1808
Brian