Thank you, brother. I have studied this issue more extensively than the average American layman, and I can find no fault with what you have written. I would have used stronger language, probably. Anyone who does not know or care who Thomas Paine was does not qualify as an informed -- or patriotic, for that matter -- American in my eyes. And Jefferson was about as openly contemptuous of religion as it was possible to be and still have been a valid political force.
The Cowboy Hat in the movie asserts the common myth that America was founded upon Christian doctrine and the Bible, which is an outrageous falsehood. While the Declaration of Independence does indeed mention a Creator, it is important for people to realize that the Declaration is is NOT a governing document, which is to say it is not legally binding in any sense upon American citizens, nor does it put forth law. The Constitution, on the other hand, IS a governing document, which IS legally binding upon the citizenry and does put forth legal prinicples, and I challenge anyone to find a single mention of God in it. Happy hunting.
What is irrefutable is that America was founded as secular nation, by definition. The First Amendment determines this in (perhaps too) concise language.