All a dog's dinner really.
The baggage - well this is a health & safety issue. The allowances are clear and to avoid handlers being off for months with injuries from trying to lift excessive bags. In the end BA waived the excess so in my eyes it was resolved. Ok, a supervisor was called, but that is what supervisors are there for.
On the seats, well to this day I don't understand why the passengers were shifted. Someone with greater need? Systems error? The difficulty here was that trying to resolve this on the day wasn't easy, as it meant shifting other passengers who may well have objected. I imagine the crew, gate staff etc saw it as a no-win situation, someone would always have been unhappy, add to this the fact that BA culture is not a 'can do' one and the inevitable outcome was reached.
Frustrating for the OP but I fear the story has reached the inevitable end.