Didn’t mean to offend , but there is a reason why some wag called the Public Schools the Established Church of the United States. My point being they are as organizationally integrated as the Catholic Church, despite appearances.
You went through all that merely to claim that the Pope’s Catholic priest, is the same as any teacher, in any school, in America?
A teacher, any where, of any kind, equals a Priest? That is laughable, I don’t think that Catholics who are school teachers would care for this route that you are taking, I doubt that Priests would either.
Aren’t the Orthodox similar to the Catholics? Why not use them for a justification?