I just tried to make a dummy reservation, and the Sheraton FRA rooms available. I also called SPG, and she said "plenty of rooms" available. But they are in the Euro 170-200 range.
It is a nice hotel, nothing special. Rooms nicely furnished. The greatest benefit is the location. You simply walk across the bridge and you are in Terminal 1. Because of the convenience, they know they have a captive audience, and they charge more. The same hotel, not located at the airport, would never command such prices.
Don't get too far away from the airport, since you have such an early departure.
LOL----we will be at the Sheraton FRA the following night.