I think they used to have a FAQ that covered your exact scenario but I can't find it now. From memory it said that the Airpoints that would fall into the >4 year category expire on your next anniversary date - so depending on when your anniversary is, you may have almost a year to use them. That would seem to match up with the credit card benefits site and T&Cs.
From
https://www.airnewzealand.co.nz/airp...and-conditions - Your Airpoints Dollars will remain valid for four years from the date they were accrued to your Account. Following four years from accrual, the Airpoints Dollars will expire and be removed from your Account on the anniversary of the day you joined the Airpoints Programme.
Unless someone else interprets that differently. Given the large balance you've got, it's probably worth a message to them to double check.