I have used antibacterial soap since I've had birds to wash dishes with, I'm not sure what the problem is with it. That article makes it sound like your birds are going to drop dead immediately. And I don't think using it once or twice on a wound is going to hurt them, and in fact could help with "R" wording the bacterial growth. Obviously you want to rinse well with hot water for the dishes and also rinse your birds boo boo well after washing it.
Which vet are you going to see? I don't think I would ever go back to the inexperienced young woman, but would head for the U of K guys making sure I didn't have a vet in training.
Ginger