Chef, we went through the same with our son and you are spot on about loving the man he has become. It made T1 put a lot of things in perspective.
As far as the out of pocket goes, we did the same with ours because school doc's really mis diagnosed everything. We went out on our own and kept our ins company informed every step of the way and they contacted the school to get second party payment info for the doc we went with. It wouldn't have mattered because like you we would have paid whatever it would have cost, well been on the payment plan like you, but regardless would have done whatever it took.
Maybe talk to your rep and see what your options are. The only out of pocket we had was $100 for the anistegiologist. Everything else has been covered between our ins and the schools. He even choose not to go back to that school and had follow ups for 3 months after and not any bills.
Good luck! He will be dying to hold a baseball in a week.