This song should definitely be of interest to NZ-ers, apparently the disaster sent shockwaves round the British Empire at the time. There's a chapter in the book "White Wings" (about NZ emigrant ships) concerning this incident.
For a melody, I've been trialing one in the Greig-Duncan books (where this song is found without a tune). It's from Greig's same informant and is goes with a song called "The Loss of the London" - another emigrant-ship-disaster tale. It's a cracker of a Scottish melody and requires only one small alteration to fit the "Scotch Patrick" words. Worth hunting out.
By the way, I think that other thread is about a completely different song, an English ballad called "Gil Brenton" (Child 5).