When there is a schedule change and the auto rebook does not suit you (whether, as here, because it does not work at all or it is simply not your choice), it falls to you to ask for something better.
Do not call AA until you have done the research to figure out what you want. Then call AA and ask for the specific flights with dates and numbers. AA will rebook onto any AA flight with F availability. It will also almost certainly be able to obtain space for you on BA.
But, it really is in your hands.