Far too much is made of the Deism of our Founding Fathers. Deism was a religious fad that swept through the colonies during the latter half of the 18th century and it died out about 1810. The Deists held to the basic tenor of Christian principle and were frequently devout in their own beliefs. The Founding Fathers were very concerned that American society was and would continue to be Christian as they felt it was the single thing that us allowed the freedom to pursue happiness.
Any reference to our Founding Fathers being atheists, or somehow less that devout is absolute claptrap.
I agree with everything you wrote, except the assumption that The Founding Fathers (I prefer Framers of the Constitution) are monolithic in thier thought. As individuals, I suspect there was some variation in thier ideas.