this is unfortunate, but if I were you, I would book this through a proper TA. They are usually slightly cheaper than NZ direct and may also hold the fares for slightly longer.

agree that AirNZ multi stop booking engine is not the best, mixing classes is quite impossible and often very stingy. I have booked through CX with multiple stops and they are generous enough to flow in Y+ for stop overs.

Air NZ always put you back to Y when you book Y+ even when the other carrier has Y+

in general, your fees should be waived based on my rule of thumb - that is, if you cannot do what you want to do, then it should be waived, however, if it was possible but you just do not want to do it, then it is fair for them to charge. This is my 2 cents and i accept if anyone else disagrees.