Your initial consult sounds pretty standard to me. Most surgeons will not give you a detailed plan with dolphin imaging etc. until later on. In private practice, most actually will charge you out of pocket to do a full work up. With one surgeon I was quoted $850 to do a full work-up with dolphin imaging, and another doctor wanted to charge me $575 for the full workup/x-rays and treatment plan. I was told it can take up to 4 hours to plan a surgery on dolphin in order to fully consider all possibilities. Usually the first consult is to give you a general idea of what they think should be done and whether jaw surgery would benefit you.
Unfortunately most "elite" oral surgeons are out of network with insurance. What that means is you pay their fee up front, and whatever insurance ends up reimbursing is refunded to you later. I would say the average surgeon fee for a private practice top surgeon is $23,000 and up. The alternative is to go to an in-network public hospital where they will not charge you anything out of pocket (which you already know about).
As for insurance, it sounds like you will probably be approved based on the severity of your open bite. Aetna will cover surgery for anterior open bites greater than 2mm and you have 10mm open bite. My surgery was covered as a skeletal deformity greater than 2 standard deviatons from the norm. I think they diagnosed it as maxillary hypoplasia. I would see if you can find the Cigna clinical policy bulletin for orthognathic surgery which should outline under what circumstances they will cover the surgery.
Also, you need to find out if your plan specifically excludes orthognathic surgery. Some group policies will specifically exclude the surgery and so even if it is deemed medically necessary they still will not pay. The pre-authorization process is something that takes a while to do and the insurance company generally wants a ton of information. For me Aetna wanted X-rays with analysis, dental molds, orthodontic treatment plan, letter of medical necessity, Cephalometric tracings, photos, etc. I think pre-authorizations are good for 6 months to a year, so I think it would be possible to get that figured out before you put braces on. Once you get a pre-authorization and it expires I think you can just request an extension.
The next step for you would probably be to decide on an orthodontist and then they will meet with your surgeon to determine how to begin treatment. At this point I would submit all the stuff to the insurance to get the ball rolling on pre-authorization. Aetna actually requires that you get pre-authorization BEFORE you get your braces put on. But every insurance company is different. It is actually nice to know that your surgery will be approved before spending 6k on braces.