“I can’t even get a straight answer if the anesthesiologist and recovery room staff are on hospital staff or paid contractors (which my insurance won’t cover.)”
At least for the anesthesiologist, they should have a list of those who are under contract with the hospital. But, overall, maybe call BCBS, I have them too, and I remember being told not to worry, as long as I use an in-network hospital.
Just becuase you use an in-network hospital doesn't mean the anesthesiologist, recovery room nurses & staff, etc.. are also in-network.
That bit me in the ass when I had to have wrist surgery to re-attach my right wrist back to my arm with two titanium plates and 12 screws. $8k worth of bit me in the ass.