I must admit, ITN does seem to show class availability correctly, including on connections. (Availability on a particular leg may be different when it's part of a connection vs. by itself.) I was a little skeptical about AA flights since ITN is not the native system, but I randomly compared a few flights on easySabre and ITN, and they matched. So while you can't book the class you want, you can at least know what to ask for when you call the airline.