Right.... having gone through all of this I have found something new from the NZ records. I found a newspaper article which I thought was about the death of Sabina (nee Francis) but was in fact another Sabina whose maiden name was Burke and appears connected to our Burkes by marriage:
http://paperspast.natlib.govt.nz/cgi-bin/paperspast?a=d&d=BH18960915.2.10&l=mi&e=-------10--1----2--From this I gather that the aforementioned Toby Burke (b. 2/10/1835) married a Burke, here in NZ:
BURKE, Tobias & BURKE, Mary
RGO 9369/1871
and Mary's sister is the Sabina Burke mentioned in the article above. This is her marriage:
HYNES, John & BURKE, Sabina
RGO 1795/1890
Married 29 Dec 1890 in Milton, Otago, New Zealand
Sabina's parents are listed as William Burke and Mary, whose maiden name appears to be either Walter/Walters or Lualter/Lualters.
Now I'm wondering if Toby and his wife are related!