How to file a compelling out-of-network clinical referral request?

Hi everyone, basically, I have found a very good surgeon to do surgery for me. Unfortunately, he is out of network of my UHC insurance. And he charges about $~60K as surgeon’s fee. 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). 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.