Indeed, they do have a shuttle bus to Fiumicino for 3 euro, but the earliest shuttle each day leaves at 8:30am, and with morning commute traffic that would not necessarily have gotten us to the airport in time, so we came up with another plan: take Castelfusano's free shuttle to the nearby commuter train station, take that train a few stops towards Rome, get off at Ostia center, and catch a public bus.
We got the 7am shuttle bus, a 7:13 train, and were in Ostia center by 7:25. Ostia is very close to Fiumicino, but the co.tra.l bus meandered its way first through the center of Ostia, then Fiumicino (a town as well as an airport location) before dropping us off at the airport in front of a daunting series of terminals. None of their signs said "American Airlines" so we asked, and were directed to get on the airport terminal shuttle. As were people taking US Air, Continental, and others that were listed on the signs.
According to a bit of fragmented Italian conversation I overheard on that airport shuttle, a brand new Terminal 5 had opened just one week earlier, and all flights to the USA now depart from there. This is apparently because the US was dissatisfied with security at the rest of the airport.
After a private shuttle, a commuter train, a public bus, and an airport shuttle, we reached Terminal 5 and quickly found American Airlines check-in. Well, not check-in exactly, just some booths where they checked our documents and determined our worthiness to enter the USA. Then through some doors to another big hall, and there was check-in... where they checked our documents again, checked our bag, and gave us tickets. We were told to go to gate C25, directed through another door... and herded with the rest of the USA-bound travelers onto a bus.
Everyone got off the bus into another airport building, where upon entry we saw a great big map of this new terminal with its gates numbered C20-C33, and up the escalator we went... not to the gates, it turns out, but to a platform to catch a light rail. As far as I could tell, the structure we were in served no other purpose than to be a transfer station between the buses and the light rail. Everyone got on the same little train, which had only one other stop: the actual C20-C33 gates structure.
Despite all of this, we got to sit for over 45 minutes before boarding. The agents at the gate checked our passports again (passport check #3) and, after not choosing either of us for the random extra screening, allowed us to proceed down the normal-looking gate extension, onto the plane. Err, no, that would be too simple. First came passport check #4. Then: another bus.
(We're at JFK now, where there's real Internet. When we got past passport control & customs, someone tried to offer us a shuttle bus.)
Edit: Home! Transport used: Private bus, commuter train, city bus, airport shuttle bus, airport bus 2, light rail, airport bus 3, plane, plane, private car. #1 through #8 to leave Italy, #8-10 the rest of the way home. Goodnight!