Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
All AAdvantage elites -- even lowly Golds like myself -- are exempt from the $75 close-in award-booking fee.
+1 to the suggestion of using BA Avios for this short, nonstop flight.