Quoting from the Baring-Gould note provided by Malcolm Douglas and Masato Sakurai, above, "But the earliest form of the air is J. S. Bach's Comic Cantata, where a peasant sings it." [Cantata 212, Mir hahn en neue Oberkeet]. If Lewis Edson didn't set "How Tedious...." to the aria from that cantata, who did?
The popularity and widespread use of Bach's music in both church and secular settings causes me to doubt that Edson would have been ignorant of a body of music that church musicians knew at the time (and still use regularly).

The Music of the New American Nation, vol. 3, Sacred Music From 1780-1820, New York Composers, Collected Works of Lewis Edson, Lewis Edson Jr., and Nathaniel Billings, edited by Karl Kroeger, probably has the answer to this question, but it is not available in the libraries here. (mentioned in thread 48046) How Tedious