For a quick update: I'll be getting a brand new phone. Have to wait unit stock is in-store at Costco. Buying this phone at a Costco kiosk has turned out not to be a convenient as I thought. Next time, I'll deal directly with the store.
Although they were going to replace it even without seeing the defect, it obligingly showed itself to the AT&T rep while I was on the phone with the warranty people.
Thanks everyone for your advice! If I hadn't asked I probably would have missed the 14-day "buyers remorse" window to get a brand new phone. After that, I'd get a remanufactured phone. No thank you on that one!