I had no insurance as I couldn't find a company that would cover me for any treatment as it was all 'pre-existing'. My surgery was covered by medicare. I think because I was born with messed up jaws and it caused me a massive amount of pain.
I have actually had braces twice. The first ortho tried to fix my problems without surgery. I didn't pay for thos braces as I as a child. I have however, paid all out of pocket for wisdom teeth removal (5, thats right), gum surgery for gum recession due to 5 years of braces, and the second set of braces. All that cost me about 15000-18000. I pay a portion of consult fees for the surgeon as well. I think they were only about 100 each time.
As for this second surgery, it will be medicare again. This second surgery is simply due to my ortho closing gaps that he said he wouldn't close after the surgery. My bottom jaw was moved forward about 7mm in the last surgery. It sat perfectly until ny ortho began moving teeth months after surgery. It now needs to be moved forward another 5mm. I'm lucky and don't need braces again this time.
My surgeon does a lot of surgeries a year. Everytime I'm there I see people who have had surgery or who are going to have surgery. Not sure about your surgery in particular. You could call reception and ask. They are very nice.
I'm actually oveeseas at the moment but I will see if I have any photos from before on facebook.