Insurance question - you'll have to call your insurance company and ask them. All policies are different; all policies cover different things. They may not want to cover a procedure in California if there is a place closer to you for the same procedure. You never know. Better to ask than get a large, unexpected bill that you have to pay out of pocket. AN surgery is expensive.
I don't know of Dr. Babu personally, but I do know that at one time - in the very recent past - HEI (House Ear Institute) and MEI (Michigan Ear Institute) were supposedly ranked #1 and #2 in the nation for AN surgery.
I say "supposedly" because I never saw proof of that.
I've heard nothing but good things about MEI and if I hadn't found a doctor close to me in suburban Chicago, I would have gone there. I couldn't imagine traveling as far as California to have AN surgery. But that's just me; obviously, others have and they have been happy with that choice.
Jan