I went through the same thing with my knee surgery(ACL, LCL, and Meniscus), doctor, network crap...
Went entirely in network but still had to fight the bills off left and right.
The two biggest problems were balance billing by the provider even though they are bound to in-network rates and the old "it wasn't pre authorized" line; for things like when I was just about unconscious and the anesthesiologist asked if I want a nerve block too...
Good luck with your surgery. Mine was a full sixth month recovery.