I can't answer you on DME but did want to comment on the Hyatt.
We are on the west coast too. Our last trip American cancelled our flight and we did not find out until we got to the airport to check in. We were not flying out until the next morning so we stayed at the Hyatt in the Orlando airport.
That Hyatt is GREAT!
The rooms were nicely appointed, the staff was incredible and the pool on the roof was too much fun for the kids. it was not noisy at all in the rooms (one of my big fears).
The best though was the next morning. The bellman came to our room, loaded up all the luggage, took us down to the American counter, stayed with us through check in and then hauled everything over to the security scanners. It was great not to have to run around like crazy people trying to get out of our room in time to get to the airport and then not having to deal with juggling bags and small children.
After that experience we have decided that from now on our last night in Orlando we are always going to stay at the aiport Hyatt. We were SO relaxed the morning we flew out - it made having to leave Orlando

a bit more bearable
Flying into Orlando we do red eye flights out of San Francisco and arrive in the morning. But I can see if you were arriving really late wanting to do this. If DME will pick ya up the next morning do it! Oh, and make sure to go for a swim on the roof!
