I assume you don't also have a Chase Ink card? My Ink Bold turned out to have the best rental insurance out of our 20+ cards - it included primary coverage in other countries.

I'd call the benefits administrators and ask them specifically what they do and don't cover. For the CSP, that's 1-888-320-9961 (per the benefits guide). They were extremely helpful when I was researching last year, and went so far as to send me a personalized letter putting my exact coverage in writing.

I assume Discover has a fairly similar department, who should be able to do something similar for you.