A TRUE STORY- CALLED MOLLY BAWN was collected and arranged by "Duncathail" (suggested by Dunkettle), whcih was the pseudonym of Ralph Varian, of Cork, author of some poems, and of a Life of "John and Henry Sheares, and editor of "The Harp of Erin," and "Popular Poetry of Ireland."
This version seems like a broadside or chapbook copy that's been rewritten by Varian- not traditional.