I think the phrase, "establishment of religion" means something different to you in the modern era than it meant at the time it was written. The phrase originally meant ecclesiastical control over Christian institutions, doctrines, disciplines or practices, NOT religious SPEECH by agents of the state. Additionally the words used by Jefferson, "religious institutions, doctrines, disciplines or practices" were imbued with the specific theological meaning of the Christian context and millieu at the time, and it is mistaken eisegesis to simply read into them the modern, more generic meaning. In other words, the phrase "under God" would NOT have been considered by the founders as establishing ecclesiastical control over Christian institutions (intermeddling), doctrines, disciplines or practices, favoring one denomination practice over another, because all Christian denominations believe they are under God. So to answer the question, it is unimaginable that the Founders would have considered a state teacher requiring her pupils to recite the words "under God" in the PoA as unconstitutional, if for no other reason than they thought the national government had no jurisdiction in such matters, not to mention the previously mentioned mistake of interpreting an historical text by mere reading into it of one's own, modern ideas.
I think the States are, under the Constitution as it was written, free to establish State Churches. I don't think it's a good idea, but if they want to amend their State Constitutions, they are, or should be free to do so. I personally would not like my State government to establish ecclesiastical control over churces, church doctrines, church discipline, or church practices. And I am absolutely affirmed in my belief every time I have to go to the state license bureau. But that is a completely different matter than a government school teacher uttering the phrase, "under God" or requiring her pupils to do so.
I think it very ironic that the 9th Circuit, which is part of a branch of the national government, has twisted the meaning of the First Amendment into its exact opposite by in effect proclaming that they have secret theological knowledge about what is "religious" and what is not, and that they, the national governnent, not we of the several states, will arogate to themselves the jurisdiction explicitly denied to them in the Amendment to act as infallible national school and theology board, determining what speech we and our children and state teachers can utter, and what speech is forbidden.
Which is why I included the quote from T.J.:
""The germ of dissolution of our federal government is in . . . the federal judiciary; an irresponsible body (for impeachment is merely a scare-crow) working like gravity by night and by day, gaining a little today and a little tomorrow, and advancing its noiseless step like a thief, over the field of jurisdiction, until all shall be usurped from the States."
Cordially,