Out of the secular sources Warren cited, two are available online. One is Amos Sutton Hayden’s The Sacred Melodeon (1849). In fact I came across this one some time ago and downloaded it then. As Warren explains, Hayden was a Disciples preacher who had this idea that if you invoke God (“the Author of his being” and “the Most High” as Hayden says) while you’re learning to sing, you’re taking “his sacred name in vain” because you don’t know how to sing the song right yet when you’re just learning it. Or something like that. So this collection, and another of Hayden’s tunebooks called Introduction to Sacred Music, despite the word “sacred” in the titles, usually avoided saying “God” and “Jesus” outright. A lot of the songs are ones familiar to Sacred Harp and Christian Harmony singers, which too use a lot of language like “Author” and “the Most High,” but Hayden did so even more. So, for example, where “Exhortation (First)” in The Sacred Harp says “Up to the hills where Christ is gone To plead for all His saints,” the same song in The Sacred Melodeon goes “The world, at each returning day, Awakes again to light.”

Source: The Shape-Note Notebook: Secular Music in Shape Notes, by David Warren Steel

* The Sacred Melodeon full book scan on Archive.org.