I'd doubt 1888 as a date for Athenry to be written, but it's be quite a reasonable date for a song written earlier to get put into print. Again, the term "broad sheet" can be used in a very loose way sometime to cover just about any relatively informal type of publishing.

Anyway, I'll be interested to hear anything John Moulkder digs up. Strikes me it's be a good idea to ask Pete St John, because he should know. (Alright, you could say he has a vested intyerest in saying he write the words rather than adapted them even if he did adapt them - but I think it's best to assume people are honest about these kinds of things to start with.)