I ordered the thing a 2nd time (this time while logged in with an SE account) and got an e-mail. If I see anything regarding the other order attempt, I'll promptly cancel it to ensure someone else isn't deprived of their copy. I'm starting to wonder if it falsely showed me a Transaction Complete type page but didn't process the order because I wasn't logged in with an SE account. Either way, I'm glad that's figured out.