Malcolm, you come down hard on lack of rigour in others concerning dates or origins of songs.On this occasion it is time to jump on you: you refer to "later accretions", ie lines which occur in an 1881 version but not in one from 1790. You know as well as I do that the fact that those lines do not appear in one version printed in 1790 has no bearing whatsover on whether they existed pre- 1790 or not.You may be right in your guess that they are later accretions, or you may be wrong. The fact that they don't appear in that 1790 version has no evidential weight one way or the other.
Say, by all means "In my opinion they are later accretions and my reasons are thus and thus". But you can't just state it as a fact. In my opinion, the 1790 and 1881 versions are from separate strands in the development of this rhyme, not two points along the same strand.

thus".