You can do a lot from New Zealand. You have access to the local records for places, births, deaths, marriages, military records etc. Have you tried contacting a local Family History or Genealogical Society for help in finding local resources to help you fill in the places? The BMD certs ($$$, of course) have to be budgeted for. I'm in the US researching Australia and there is a lot I can do from here.
Check out www.cyndislist.com for a lot of links by category. Also see what FamilySearch.org has for NZ records. Their Wiki may helpful and the catalogue will be very helpful. Are you within about an hour's travel from a Family History Centre at an LDS church? Being local people they will be very helpful for local resources. And if there is a film at FamilySearch you need for your research you can rent it and have it sent to your nearest Family History Centre. They can tell you all about it. Just be sure to call before going to find out when they are open because they are staffed by local volunteers and the hours change.
Most libraries have either Ancestry or FindMyPast available for use by their patrons. FaceBook probably has NZ genealogy groups; there are a lot of Australian ones there and they can help you find resources accessible in NZ.
Please forgive me if you've tried all of this. I'm not sure what you know and the sources on the profiles I looked at I couldn't access.
Working further back really can't be done reliably until you've filled in a lot of the gaps in the later generations, particularly about where they lived, worked, and went to school. People didn't live in a vaccuum; they left a trail of breadcrumbs on their surroundings and it is up to us, the genie mice, to find them and gobble them up.