I came to the same parody conclusion, but from a different angle. I was investigating the tune of a Yorkshire version of the song, and found that the tune is the chorus of a 'minstrel' composition 'Nellie Ray', composed in 1865 by American Violin player and 'Minstrel musician' William H. Brockway,(1835 -1888). Another sentimental song crying out for a parody.