Though a number of Ingalls' works appear in shape-note books, Ingalls collection The Christian Harmony was written in standard notation--he was not a shape-note composer, per se. His book should not be confused with William Walker's shape-note collection Christian Harmony, published in 1866. To muddy the water further, an edition of Ingalls' Christian Harmony was published in 2005; for it, the editor used shape-note format--historical revisionism at work. They also put out a CD recording of selections; see: http://www.singingalls.org/Commerce.htm

The 4-shape system first appeared in 1801, in Wm. Small and Wm. Little's Easy Instructor. But the golden age of shape-note singing ran roughly from the 1820's until the Civil War, and was concentrated in the South. The most popular collections didn't appear until this time, for instance, Southern Harmony (William Walker, New Haven, 1835) and The Sacred Harp (Benjamin Franklin White and E.J. King, 1844).
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I was a bit confused by Q's citations; the song "Liberty Tree" has no relation to "The Appletree" that I'm aware of, nor did the Boston Camerata combine them in any manner on one track.

The Camerata recorded the song "Liberty Tree" on the album Liberty Tree, track 3. On The American Vocalist, they sing "I Shall Be Satisfied" (from The Revivalist), which was set to the same tune as "Liberty Tree". A similar contrast of a secular song reset with a religious text occurs with LT track 19, "Working Boy", and AV track 15, "Go Worship at Emmanuel's Feet". Religious fervor excuses all manner of corruptions, apparently.

They recorded "The Appletree" on Liberty Tree, track 8. In the liner notes, Joel Cohen says that this tune began as an instrumental march but doesn't specify whether Ingalls wrote or merely arranged the tune. And though their source was The Christian Harmony (with Smith's text), they perform it as an instrumental.