Nope, don't give in. Do what we do at the 'Friendly Skies': Hang up and call again.

I pulled up a radom date (16 Dec) and the flight at 1800 GVA-LGW is showing J9C0, but the seat map has no one booked. Strange as the flight before is J7C7, with no one taking a seat. The LHR flights, by contrast, show loads of availability.

So I think it is the yield management trolls playing havoc with you. As I said, keep trying. BA changed the schedule not you. Oh, and watch things come end of October, as they may change then as well.