Hyatt has an alternate way to verify your identity through an email process. I did it at the DFW Grand Hyatt. I had to push, but it happened. I REFUSED to use another card for that exact reason. He told me I could call Hyatt the next day, but seriously, I wasn't risking it. So he sent me an email to the email on file, and I verified all my info and sent it back, right at the desk. It went through since I knew the answer, and worked for the incidental charge, room service, and everything else. So push for that. It's Hyatt, not that specific hotel, which has that.