Call the hospital and offer to settle. They will cut the price almost certainly. Almost anything they can get you to pay will be more than they will get selling the debt to a collector.
Thanks for the advice. If all of my appeals are denied, I will follow it and try negotiate the price down. In any event, this won’t be a catastrophic financial event for me. But it sucks that it is happening to so many people under our current insurance regime, and not not all of them can handle it when their insurance decides not to pay.