Anyone have experience with booking day rooms at Marriott hotels in Doha?

Arriving on an early flight and leaving 20 hours later. Sharq would be my first preference (being close to DOH) but was advised they "don't do day rooms" - with no alternative option offered.

Thinking I could potentially book it the night before and request a late check-out...but still leaves me checking out about 10hrs before the flight assuming I can even get a 4pm check-out. (I'm Gold).