"no foreign fee credit cards AND primary coverage"

Not sure that is correct, not positive at all, but I have a diners club card and benefits from way back when .... only reason I stil have it and pay the annual fee (now I might be grandfathered also for the benefits, that I do not know). But it provides primary coverage worldwide (some exceptions, but not sxm) and do not remember (can look) about a transactoin fee, but know for a fact that there was no transaction/exchange/conversion fee on our last rental.

Now in the US, diners club is part of MasterCard.

Yes it provides "primary coverage, even in the US" I do not rent a rental car anywhere in the world without using that card. And yes I have used it for coverage.