You can also just call the AA Around-the-World desk. They are VERY good, in fact much better than BA, IB, QA, CX and others that sell the exact same tickets.

The number is: 1-800-247-3247 7am-7pm CST

Also keep in mind that the fare is determined not only by number of continents and class of service but also country of origin (and the differences can be huge)

Have fun touring the world.