I'm leaving my Puritan comfort zone to actually address the Founding generation (though my readings in the field of scriptural translation spring from my study of those Bible-reading people). Trying to identify the religious beliefs of the Founders provokes nearly unending debate; what I'd like to investigate here is the religious scholarship the Founders may have read that may have formed some of their religious education.
In 1707, John Mill of Queens College, Oxford published an edition of the Greek New Testament that took the 1550 edition written by Stephanus and then listed all the variant readings of that text in a critical Apparatus. Mill found 30,000 differences between the translations, places where different manuscripts of the New Testament over the centuries provided different readings from the "received text" of the scripture.
This was, of course, controversial in England and Europe, where Protestants found the validity of their religion on its basis in scripture. If there was no final scriptural word to be had, no text that really had the exact word of God in it, but only many human variations on a theme, then the Catholic insistence that scripture could only ever be one part of religion was validated. The Catholic church had always averred that church custom and practice was more important than scripture, and this unreliability of scripture seemed to prove it.
Mill's work put in motion critical examinations of scripture that made the 18th century a century of exegesis. Notably, Johann Albrecht Bengel and Johann J. Wettstein both explored scriptural variants further, and Wettstein published a new edition of the Greek New Testament in 1751-2, showing even more Greek, Roman, Jewish, and catholic variants in meaning.
Each of these publications provoked a firestorm of critical responses. The 18th century was the age of the pamphleteer, and because the religious stakes were still high in England in the first part of the 1700s, each new publication was capable of arousing great public praise or indignation.
Laying out the differences between translations of the Bible, some of which crucially changed the message of the scriptures, clearly led many people at the time to lose faith in the Bible as the received word of God, and even their faith in God. If two of the gospels had originally made no claims that Jesus was God, if those claims were added in by later second- and third-century scribes who wanted the Bible to say Jesus was God, what was the basis for faith in Jesus? If God did want humans to know God's word, why were our versions of the Scriptures so clearly humanly rather than God-generated?
The work of uncovering more and more early translations of the New Testament would go on in the 19th century. Our Founders, who were well-read English-educated and oriented men and women, must have been aware of these debates and findings in their own time. They must have read and pondered Mill and his many critics and followers, and perhaps even read his Apparatus, or the scriptures of Wettstein. It would have fit their Enlightenment bent to question and even reject scripture as a useful religious guide. And it might have led some of them to deny the divinity of Jesus.
I would love to hear from those readers who have more in-depth knowledge of the Founders' religious reading to see if my theory is correct.