Without details of what info was contained in the booking it is hard to be certain but on the face of it the presence of a wheelchair should have alerted the airline that articles 9 and 11 of EC261 may well come into play. It is also unclear whether the airline sought volunteers under article 4 before offloading the OP.
Unfortunately seats do break from time to time but for the staff at SJC to wash their hands of the OP is quite unacceptable.
It sounds like the priority should be to focus on transportation back to the UK and then a serious discussion with BA should take place. There are legal options available and it is the type of case involving travellers with disabilities that the media may well be interested in.