Sounds as though you should have a day away from family history

I think the only way forward to establish the DADY/FORD/COX facts is the marriage cert in NZ showing Henry and Mary's signatures and then hopefully, a couple of certs from Victoria or the one from NSW, which will have signatures of Mary at least.
I was thinking about the DADY birth registration in 1888. I wonder when registering Amelia in 1888 the local registrar may have asked the following -
* name of child ..... Amelia Frances COX
* your name ...... Mary Elizabeth FORD ... whoops

* and your former name ...... DADY.
And then it may have become a little confusing for Mary so she didn't name the FORD father as she had just named the child Amelia Francis Cox FORD/DADY.
As I always told my children....if you are going to tell fibs, you need to have a very good memory.
Cheers
Cando