I think you've done a great job articulating this issue. Full disclosure, I am an atheist and personally prefer ending invocations at public meetings, but I certainly have no problem if individuals or groups of individuals choose to exercise their religious freedoms to pray for guidance. I think those that choose to should have the opportunity and perhaps allotting the normal invocation period for a moment of silence/reflection might be better; this would allow those who choose to pray to their respective deity or deities on a personal level.