The 'cuckoo' image is often used as a 'floater'; an often unrelated verse which is tacked on to a song (Bee's version, which is similar to Clarence Ashley's is virtually made up of 'floaters'.
The cuckoo motif is best known in Ireland in association with the song 'Bunclaudy'.
IMO the image of 'sucking on small birds eggs to make her voice clear' in 'Nutty's' version is one of the most beautiful to be found in folksong.
Jim Carroll