Gave Air New Zealand a call, and glad that everything is sorted out!
The call agent was extremely helpful - there was no need to negotiate or to plea or whatever!
So I got a new flight and everything is alright!
There seems to be some major shifts in the Christchurch to Auckland flights (direct and via Wellington) though! I was looking at my screen while talking to her, our flight schedules don't seem to tally. Wonder what's happening at Air NZ?
But glad everything's fine now!