I'd take a REALLY cheap room -just for the shower-by the time you've eaten and showered it'll be time to go back to the airport anyway but you'll at least feel refreshed. I've paid something silly like sub $20 for Imperial Palace in the past -had no intention of using the sub-standard bed just wanted a base for a few hours and it fitted the bill.

I don't think sleeping at the airport would be "awful" just a bit random -all you need is a few drunks doing what you are doing to make it an annoying and sleep free experience-assuming you can find seating without arms away from the banks of slots.