Follow up:
While my local big-box stores only carry plastic-capped roofing nails up to 2”, they did have a box of hot-dipped galvanized metal plates hidden way up top near the roofing screws. Was pleasantly pleased with the price ($3.80 for a 1lb box... which appears to hold maybe 100 of these thin metal plates).
So basically I can mix/match screws/nails with these plates. Problem solved.
Also had a mini-stroke going through all the different types of construction adhesive/caulk. First estimate is there’s more than 50 varieties. Again, found PL-300 and it seems to work as it should. I almost bought PL Premium which also said it could be used for rigid foam boards, but then saw a box of the PL-300 Foamboard Adhesive way up on the top shelf.
Trip to the store took me almost an hour, mostly searching for the nail caps. Actually insulating the space (two layers of Polyiso - four sheets total) took me about as much time. Go figure ;-)