Originally Posted by
Calchas
Well I've taken the liberty of checking the loads on this day --- every flight out of there including connections is fully booked (and likely oversold).

I can only hope that they bagged a final two seats for you.
I think it's far too early to say that the flight is oversold, even if it might currently be overbooked to the overbooking limit.
The fact that most of the BA codes are 0 rather than C, and that the IB code still has L in some classes, suggests to me that revenue management could well make seats available, particularly if BA understands that it's a BA stuff-up.
It's a pity that connecting in the US isn't a viable option, as there's plenty of space on AA's morning flight to MIA on 28 April. It wouldn't be ideal, but it would be a useful backup to have. But BA should be looking after the OP one way or another.