Okay. I was able to get Orbitz to pull up that fare. I had to enter in the multi-city query exactly as I did on ITA.

Resolution: I called AA.com Web Services again to point out their system was not letting me make a reservation. I mentioned that I was able to pull the fare up on Orbitz for the lower price, gave them the fare basis, and the kind lady was able to get that fare as well, fare basis and all.