I checked my copy of the Bates County Sesquicentennial book, and I find no mention of "New Harmony", however there was a Harmony Mission established in 1822 on the north side of the Marais de Cygnes. The town of Papinville was built nearby in later years. The mission was closed in 1836, the buildings sold to be used as a private dwelling, and later moved to Papinville. They were burned during the Civil War. The Harmony Mission was central to the white settlement of Bates County, and the first post office in the county was established there (Batesville). If you need more details, of which I have few, please email me off list.