If it has been ticketed the the safest answer from the call centre will be to redeposit miles and rebook. There will be a charge for this. 5,000 miles or US$50 I think)
You might be able to negotiate with the call centre person whom does the change but i think now that it is ticketed a no charge change is unlikely.
For bookings of our family I now usually split the bookings and do each person individually. They just seem to be more willing (or capable, or likely) to move and allocate single extra seats than a block of 4 for our family.
If you hvae time on your side, go back to them and first find out if J is available on that AKL-NAD sector. If there is availability then you can move forward.
Another consideration to land availability is always to be flexible with dates.
Hope that helps.