Wolfgang, I beg to differ. The song DID survive in the New World. At least in Nova Scotia it did. There is a version, which Clary Croft, Margo Carruthers, Raylene Rankin and others sing, that was collected by Dr. Helen Creighton, on the mainland of Nova Scotia. I'll e-mail Clary Croft to get more specifics about it.
Oh! I should see about typing it up. I don't think it's in print anywhere, except in the Helen Creighton Collection.