I had the pleausure of flying NZ air from cristchurch to aukland at the end of my trip. I never had the run around that you had (on the phone). Checking at the curb with a 20 is a good idea, however I didnt have that luxury. Here is what I did. while in the maze to get checked in I put my kayak over to the side of the line and didn't haul it to the check in lady. when she asked how many bags i said 3. she checked my two bags and then asked where the third was. I pointed over to my kayak and said I left over there to avoid hauling it through the line. She asked how heavy it was and I said 30 lbs (a huge lie, as it was stuffed with gear). She handed me the baggage ticket and sent two people over there to carry it. No questions asked and even better no charge. This method of leaving the boat to the side worked well. I used it on my flight with Pacific air to Fiji then LA with no charge (they charged me $150 on the way there) and I even used it with frontier for my trip from LA to denver (again no charge). So my boat got a free ride home. Deffinately use a boat bag as it disguises the true nature of your luggage. One note. I was paddling an eskimo diablo which is over nine feet long and I had no problems. It will all work out for you just smile and be friendly and lie at the proper moment. As the kiwis say "No Worries".
p.s. if you are going to hokitika look around for Garroth he is an awesome boater who does nothing but paddle the big shit on the west coast. He used to live in Salida. He is a good person to meet down there.