Employer health insurance only works sometimes

Hi everyone, basically, I have found a very good surgeon to do surgery for me. The surgery itself has been approved as medically necessary. Unfortunately, he is out of network of my UHC insurance. And he charges about $~60K as surgeon’s fee and the out-of-network benefits of my plan pay only~10%. As suggested by a moderator, of this sub(, which I really appreciate), I’m filing an out-of-network clinical referral form because of network inadequacy(explained below), which if approved would greatly reduce my cost. What should I do to increase my chance of getting approval?

Specifically, I have contacted all three in-network surgeons suggested by the insurance company in the first place, and none of them actually do the surgeries. (Note: I actually called all surgeons within 30 miles of my house. Still, no one does it. All providers nearby who do it are out of network.BTW, I am in NY, but the surgeon I want to go with is in California.

I still think I am unlikely to get approval because it seems too good to be true, and more importantly, I hadn’t ever seen anyone mention this online. Also, no one ever told me this, not even the out-of-network provider for whom I am seeking the referral to do the surgery.

Any suggestions will be appreciated!

Edit: Zip code: 11720, NY. I am a Ph.D. student with minimized NYSHIP plan.