The best way to get the insurance co to authorize the visit (gosh, the
freedoms we have lost!) would be to get their surgeon to say to them that he
is not qualified to do the job on a professional singer, and the thing that
would make him say that is the fear of a lawsuit over the loss of her singing
voice.  If you make clear what is riding on the surgery, and what you will do
in the event of damage to her vocal cords, then I think he will be happy to
convince the insurance co, and they will be happy to authroize a more skilled
surgeon.