Have often found NZ to be flexible on Non Flexible fares,

Work takes me to Christchurch often, have found on many occasions getting to Christchurch airport very early to catch the Shuttle to Auckland, for the LAX flight, they have let me catch a flight 4 hours early so I can have a few hours in Auckland on the way out. Never would push or demand for it, but just asked "Would you like me to catch an earlier flight if there is a seat to free up space on the later shuttle", and without fail they offered to change me.

Richard