Focus, people, focus.
I think the part about taking students to a house of worship with some participating in the call to prayer probably violates the Establishment Clause. When you have court decisions that breathlessly exclaim that students on the way to graduation in a church auditorium will be required to travel on streets with the names "Agape" and "Barnabas," you have to figure the courts think that students old enough to graduate from high school are completely unable to think for themselves.
That makes it pretty hard to imagine public schools doing any of this. They cannot imply support or non-support.