Minimum stay for a 30k room is 2 to 3 days, sometimes 4. Your only chance is to call Hyatt 48 to 24 hours before check-in to see if something opened up. I once got a single day at the last minute even though it was not visible on the website.
There are periods 12 months out even where I put in even 7 nights where there are normal rooms available but once I go over the weekend, it will only give me suites...