So to answer my own question, I called the GGL line, and the agent explained that with the new system... you can't actually change your seat any more after you check in even if you have NOT issued your BP. The only option she could offer was to offload me so I could check in again, something I would rather not do as the flight looks overbooked.

My only other question is whether [utter bloody] "moron" is an insult or not so as to know whether to post what I think of the BA IT people or to keep it for myself.

Oh yes, I also tried to pay a booking for over £5k and the system crashed after entering the credit card security information and nobody at BA can tell me whether the payment went through or not and all they can offer is for me to call back tomorrow to speak to the "finance people" who are the only ones to know.