Steve, I'm too musically illiterate to turn your sheet music into ABC for the interest of all, but I do see that the melody is very different from anything I'm familiar with, including the tune in Petrie.

That music, BTW, is credited to "Hermann Loehr."

Not even the stanza form is same as in "Rory O'More":

Oh! if all the young maidens was blackbirds and thrishes,
                                          was blackbirds and thrishes,
It's then the young men would be batin' the bushes.


Oh! if all the young maidens was ducks in the wather,
                                        was ducks in the wather,...
[Etc.]

One likely interpretation is that Lover gave traditional lyrics in the traditional pattern in "Rory O'More." These he adapted, with Loehr's help, into a new parlor song of his own.