I have asked a Bach scholar and musician relation of mine to compare Mer Hahn En Neue Oberkeet with the melody used in the hymn, and to find out the source of Bach's melody if possible. I hope that he will do it if he isn't on tour somewhere. Bach's music is pretty well documented in his notebooks, and the sources of most of his arranged melodies are known, but a music library specializing in the period would have to be consulted.

There is a song known as "Farewell, ye green fields and groves," which possibly could be the melody Bach arranged for part of his Cantata 212. I have never heard it. If the title is not a translation, one of our UK friends might know of it.

"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" ed. by Karl Kroeger, may have information.