If you are self pat, you really should have some kind of contract that spells out the costs and obligations on both sides - the insurance companies do that in their network contracts and it is reasonable to do so as a self pay patient. We self paid for my wife's DS and that was under an all inclusive contract that the surgeon had worked out with the hospital - all hospital and surgical fees including anesthesia and incidentals (no lingering bills for $10 Q-Tips, etc. and it seems that everyone down to, seemingly, the floor sweepers are independent contractors wanting to send you a separate bill.) Our contract also included a cost cap in the event of complications, covering additional surgeries and hospital days, if needed. As a self pay, you have the choice of dealing with any surgeon and hospital in the world; the surgeons are often more sensitive to this than hospital administrators, though I would expect in a city like Huntsville they would be more sensitive to competition than an a rural county with only one hospital.
Talk to your surgeon about this. They are often on staff at multiple hospitals, and some hospitals are more accommodating than others.
Good luck, and hope all works out...