There's no point trying to appeal to BA's better nature on this. It's a corporation, and doesn't have one.
It makes perfect sense for them to do this commercially - clearly the more stressful and long-winded they make this for you the less chance there is that any of this will end up in the hands of the regulators who do have the power to take these actions and levy fines. They basically want you to give up and go away.
Follow the advice given earlier, detach yourself from this personally, forget about dealing with BA directly any further. The time is now to clinically play hardball with them, and use any and all avenues that are available that make life as difficult for them as possible.
+1
You bring an old country saying to mind " A race horse needs a flick of a finger, a donkey needs a two by four" !