Seth:
Your insurance company wants you to go to specific places because they are within their network and meet their criterion of being "capable of performing the surgery." I heard that a lot myself. With all due respect to the doctors, my veterinarian is capable of performing the surgery but the outcome would be... a crapshoot. But for me, the point of the surgery is to wind up with an outcome that doesn't leave one with facial paralysis, speech and vision problems, dizziness, et. al.
I went through this. Here's how I got my insurance company to allow me to to out of network (in my case, to House) and pay for it.
Let's say your best chances of a good outcome are at House and JH. Ask House and JH if they will charge your insurance company the average $$ amount they receive from the local HMOs who do have contracts with them. Get those charges documented, and before you send them along to the Medical Director of your insurance company, call him or her directly and ask if the company would agree to pay the average that Calif HMOs pay House, or MD and VA HMOs pay JH. If he says yes, fax him over the rates and KEEP FOLLOWING UP. The hardest part my be actually getting through to the medical director!
The bottom line for insurance companies is money. You've shown them a way to minimize their cost while simultaneously improving your chances of a normal life. It's well worth the effort. Good luck.