Jim,
Just in case the OP is still around I've taken the liberty of extracting the crucial answer to the query from your long quotation.   'Paul Brewster has done a very complete survey of both the song and the tale in FFC, #147 (1953) and included a useful bibliography to both in Bids Sgs lnd, 42-43. He feels the song began in Norway before 1600, spread through Scandinavia, and then to Britain and the West. However, he thinks the tale is of Slavic origin'

From what I've seen and heard of the very beautiful Scandinavian versions, Norwegian in particular, I'm happy to go with Brewster. Most British versions are somewhat burlesque in comparison, although I hasten to add I love singing my local version from Driffield, East Yorkshire.