If, for some reason, you don't go through the Diamond Desk, I would call the hotel back at a different time so you talk to someone else. There is a great chance you will talk to a new person who would be more helpful. Also try calling the hotel in the late morning or early afternoon. Since the front desk is usually less busy during those times, the clerk you reach can spend a little more time looking over the reservation with you on the phone.

Report back what ends up happening. It would be helpful for people to know if the Hilton Times Square treats it's Diamond guests poorly even before they check-in at the hotel.