Hi Dean
I'm presently doing a Gibson family tree for a friend whose maiden name is Gibson, and could quite possibly be related to you. Her ancestors were also on the ship Dunedin which came over to NZ in 1874, settling in Christchurch., or more precisely Ashburton/Dromore area. I have got the passenger list from Family Search (see link below) of the Dunedin and see there were 3 Gibson families from Tyrone who traveled out here (NZ). My friend's connection is with James Gibson and his wife Mary Jane, nee Kee, (her great great grandparents) who travelled out with their three children - Anne Jane, Matilda, Elizabeth. I note on the same passenger list Robert Gibson, his wife Matilda, and their children, Pat, Matilda, Margaret & Catherine. Also another Robert Gibson with his wife Jane, who I preseume are the two you mention in 2/. Happy to share the information I have collected so far.
Have you seen this from Family Search?
https://familysearch.org/pal:/MM9.3./TH-266-11618-62212-21?cc=1609792
James Gibson's father's name was Robert (taken from his marriage record) and I'm wondering if he could be the same one that you mention, born about 1818 who married Matilda Doeherty? James was born abt 1844, so the dates fit.
Regards
Elaine