The hotels at Fiumicino know why you are staying with them. "Reasonable" may not always be available. It's a sellers market out there. Of course, Margaret's idea is excellent. Stay for less in Rome and take an early Roma Shuttle to the airport. One way or another, you'll pay an extra 40-60Euro for having to get to the airport early. It's either at a Fiumicino hotel or a shuttle.
CLICK HERE to see a list of hotels from the www.tripadvisor.com site.
Here's a post from Greg from Kentwood, MI earlier this year:
"If your looking for a clean bed, with a no frills hotel then try either the Mach 2 Hotel or the Cancelli Rossi Hotel. They are both near FCO, less than 2 miles, they both have shuttle service to FCO and the rates are a little over 100 euro per night. I stayed at both hotels and either is fine, although the Mach 2 is my preference. Both Hotels have a three star rating."
Note that at 3:00am in the morning, the hotel may have to call in their shuttle.