It is regrettable that you have already used all your appeal options.
You may have more options available to you, including filing a grievance with your state's department of insurance, but what truly matters is the wording on the actual authorization letter.
Does it say anywhere that services were to be paid at the "out of network" rate? If yes, you cannot win any appeal or grievance unless you can prove that the services were rendered in a life or limb-threatening situation.
If there is nothing indicating the level of reimbursement, you should then turn to the facility for an explanation as to why you were not informed prior to surgery that the facility was not contracted with your plan. Although it is ultimately the patient's responsibility to check whether a provider is in network, it could be considered that the facility did not act in good faith by not notifying you.
In some states, medical providers are legally mandated to give you this
information and provide you with a written estimate of the cost.In this is the case, I might advise you to file a complaint with either the Compliance Dept or the Patient Relations Dept. This failure on their part could lead to a reduced bill.
Another option is to get screened for financial assistance. Hospitals have private or federal-subsidized programs you may qualify for. Call the business office and ask for an application, or check the website for criteria.
If all else fails, negotiating a settlement is your next step. Ask the insurance if they can give you an in network fee estimate (or use the "cost estimation" tool on the website using a contracted nearby facility). If you offer to pay the full agreed-upon balance now rather than over a number of months, you should be able to wrangle an additional discount.
Best of luck!