I want to set up ns1.DOMAIN.co.nz as the name server
OK, it doesn't sound like you can.
I'll tell you our setup is that helps.
We have clearfield.co.nz setup with NS's of ns1.clearfield.co.nz and
ns2.clearfield.co.nz
We also have clearfield.com setup with NS's of ns1.clearfield.com and
ns2.clearfield.com.
For .nz domains we tell our clients to use the ns?.clearfield.co.nz NS's and
for .com domains tell them to use n?.clearfield.com.
When we have to renumber we only update the registration details for 2
domains: clearfield.co.nz and clearfield.com (as they use ip addresses), none
of our clients have to change their domain registration details (as they use
names)