At the moment, the AA site seems to have a glitch displaying all available AAnytime routings (especially more direct ones). There are a couple of options: 'put something on hold and call web services to straighten things out, or better they might be able to reserve the flights you want and allow you to then confirm the booking and pay the taxes and fees online.

As long as seats are available, you should be able to book an AAnytime award, well, anytime.

You could call reservations, but they might insist on the $25 phone fee.