I think what we need is:
The full list of children born to William & Margaret with dates/places (in order) from eldest to youngest.
The source of the marriage date/place?
Some evidence of who the others travelling were whether child/sibling/cousin or other?
Has any info. been found on any of those people?
I'm unsure what would be written on a child's birth cert. in NZ but it would be interesting to have what info. does exist?
Who was the informant on Margaret's death?
Was it a relative or other?
Names can get mixed up too over time as we never talk about our parents/grandparents by name (unless in genealogy) where/when it's necessary like now

Is there anything/anywhere in NZ which would require their places of birth which can be accessed?
Did they sign forms for permanent residency which would show their places of birth?
We need more info. from the NZ end in order to progress.
Annie
I had an alert when I was posting so to answer the alert...
Pete,
I'm aware it's not impossible as I've written on my post but others were recorded in months & I have also said errors occur.
I knew 2 siblings who were born in the same year & they weren't twins

We need you to confirm those relationships to progress....whether they were siblings or otherwise related...is this possible please?