I don't think there are any tricks really unless it's a destination that throws up the stopover option. If you have an active IB account have you tried there. If not you'll probably have to call BA.

Does it really help you to be secretive about XXX? If it's something natural like LHR-MAD-AGP (or TATL longhaul) it probably should come up and you might be able to argue the off-line fee with BA, but less so if it's LHR-MAD-ZRH for example. Are you sure the connection is time-valid?

It's probably more likely to come up on aa.com and may be better value in AA miles given the connection.