A minor clue to the sequence and dating of these songs:
In Henry Lawson's short story "The Songs They Sang" (published
in ON THE TRACK (1900), he quotes a verse of "Ring the Bell,
Watchman", but no mention of either "Shears" or "2nd Mate".
I can't think he wouldn't have mentioned the Australian
parody if he knew of it. But he is talking about the "roaring days"
of "twenty years and more ago". The story has snatches of many
songs from that time.