Wirelessly posted (BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

If you can find "MileSAAver" Coach award seats from MEM to BZE via DFW or MIA on aa.com, you should be able to secure those seats for 29K or 30K Avios roundtrip, per person.

Note that the ba.com award search engine can be buggy about finding connecting award flights on AA. You might have to call the BAEC Service Center (and pay the telephone booking charge) in order to get the awards issued.

In the meantime, you might want to try to build up your stash of Avios by crediting hotel stays, car rentals, and paid flights on AA to your BAEC account.