Hi
The following is about ruling out "the possible third NZ marriage of a Joseph EDMONDS to Anne (Annie) LONERGAN - 1884".
Just briefly,
this particular Joseph EDMONDS, a publican, died in Dunedin in 1888.
[He had a child, Ellen Ida EDMONDS with wife Annie. Annie also raised three stepdaughters, the children of Joseph's former marriage, namely Ann Jane (bc 1875), Thirza (bc 1877) and Mary Ellen EDMONDS, who appear to have had a mother named, Mary Ann.
Info mainly from the (lengthy

) Probate file of Annie EDMONDS - d. 1904. Image # 148 gives confirmation that Annie's former name was LONERGAN.
https://www.familysearch.org/ark:/61903/3:1:3Q9M-C9Y7-Y9QF-J?i=119&cc=1865481[File ^ contains Will of Joseph Edmonds also. ]
So, this Joseph EDMONDS was
not your man.

~ Lu