If you can check out BA.com, you can use the availablty tool there to get an idea of what's out there. Not sure how close AA's access comes to BAECs, but if BA avalabilty is tight on BAEC you can assume it's going to be tight on AAdvantage, IMHO.

https://www.britishairways.com/trave...club/_gf/en_gb

For 2 adults n CW, BA shows outbound open on 11/30, return on 12/9,14-16,21-23.