Welcome to Flyertalk.
Not wishing to appear pessimistic from the outset but Air New Zealand availability with VS points has always been almost impossible - I would guess that around Christmas / New Year it is going to be even harder.
If you look back on threads in this forum - partner reward flights are not always easy!
We did the trip a couple of years ago (not around Christmas) we got VS Upper rewards LHR to LAX then flew to Honolulu with Hawaiian Air - then to Auckland with Air New Zealand ( revenue seats) - we came back via Honolulu then to SFO and used VS points to get back to LHR.
Another option is to fly VS to Seoul - assuming the route starts as planned - and then get one of the Asian airlines down to NZ. Air Asia for example offer good Premium Flex deals via Kuala Lumpur.
I wish you the best of luck in your quest, but can't offer any easy option.
Nick