Here’s what I’ve done in a similar situation. I once checked in at the Park Hyatt Sydney early in the morning after a long transpacific flight. They told me they did not have any standard rooms available (I had redeemed points) but they did have an Opera View King available and if I wanted that room it would be an extra AU$100 per night for my 5 night stay. (Since they were ‘full’ they wouldn’t offer any complimentary upgrades.)
Unquestionably this is a room type eligible for elite upgrade. And by definition it was available for the entire length of my stay (as with Marriott, a requirement for Hyatt) since they were offering it to me. I was tired and wanted to go to my room, so I accepted…