From the information currently available, it appears to me that the BA crew responded to an actual loss of thrust in the most appropriate manner by retracting the flap setting to enhance the glide performance, thus bringing the AOA closer to that for "best glide."
Reaching stick shaker obviously demonstrate that the AOA wasn't controlled in a way to enhance the glide performance. Since the AP was following the ILS the AOA didn't stop increasing, very far from best glide. Retracting flaps doesn't lead to AOA reduction (on the contrary if you wish to maintain a constant path), it only improve drag.