I do not believe there are any problems with the system pressures--when I had recharged it the high side was around 200psi which was expected based on the ambient temp.
I think the issue is just a cheap aftermarket part. The schrader I purchased was this "GDP" 1311574 cap/valve kit, which I see now is identical to the Four Seasons (bleh) and UAC parts shown on Rockauto.

I can get an OEM schrader for a whopping $55 + shipping (I'm used to Jag prices after 10 years, but this is insane).

Is there a better alternative? I don't mind paying for a quality part, but I know that OEM schrader didn't cost $50+ to make. $45 of that cost is the baggie that says Jaguar. Any suggestions appreciated!
Thanks,
Michael