There’s plenty availability for today’s BA192 (B781) flight (F4 A4 J9 C9 D9 R9 I9), there is also availablilty on the 15:05 AA (77W) flight (F3 A2).

You don’t say why YouFirst were unable to rebook you, perhaps you can raise that with customer relations on your return. Did you ask AA to assist being the carrier who caused the misconnect?