Please keep us posted on how this worked out for you. I also have a high dollar deductible plan so am curious as to what happens.
In the past, my strategy has been to advise the physician or facility that I will pay once I or they receive the statement back from the insurance as to what I actually owe. I also found out from a call to the insurance company that when they contract with the providers to be part of their provider network, they are not supposed to bill the patients until they get their EOB back from them.
Sometimes works, sometimes doesn't. But haven't worried too much since I am usually dealing with small amounts vs something major like WLS.
In your case, perhaps trying to save a portion of your deductible to have ready at time of surgery as a sign of good faith would help them to then allow you to make payments for the rest.
Hope it works out for you!