I've spoken to 20 differed orthopedic centers in the region and none of their doctors will consider doing a surgery through NFZ.
Impossible. It is fully refunded by NFZ. The only problem is a long waiting time - even a few years in unlucky regions. Probably you wanted to say: none of their doctors will consider doing a surgery through NFZ within a month or two.
That would be closer to the truth.
I'd prefer not to pay out 10-14K for the cost of surgery privately
Of course, nobody wants to pay through the nose if it can be avoided. But you need to estimate if the delay won`t cost you more than 10K.