Assuming that you already have Songs of the West, I'm afraid I can't really add anything useful, as, though I have the book, I don't have the recording. Baring-Gould reckoned that James Parsons sang the two parts of the song together, but I confess to being rather dubious. I don't believe that that first part belongs to the song at all, but is a separate thing bolted onto it by way of prologue. B-G was not unknown for such things.

That doesn't mean that his was the hand that held the spanner (though I'd be astonished if he hadn't at least been at it with plenty of polish); the song is listed in Martin Graebe's index of the personal copy MSS. Martin is the man to answer the question, and indeed any other relating to Baring-Gould material. He was also one of the singers on the record, of course. He posts here as "Greenjack" from time to time.