We used to be able to just put the rifle in Baggage with our other stuff an it was known that it is a Rifle..
then AirNZ an such realised its big business and they are Charging it as you mention, Extra Baggage.
The New Zealand Laws itself and Culture, is Very Welcoming for Firearms... I mean once I had all my papers sorted on the Aussie End... I was givin a Temporary NZ license (valid 12 months or until you first leave the Country) after Sighting my Australian License, I then walked out of the airport, waited at the Bus stop, jumped on a Bus heading toward the place I wanted to go, an it was loaded full of School kids, they had a guitar and sang songs while I talked to the Driver about what I was doing and where I was going, he was genuinely interested.
I got off in town at the bus stop, my back pack and Rifle case... walked around town for a few hours then headed off.
It is what they Call, Old Australia.... we are Doomed over here now but there is still Common sense prevails in NZ, with Great hunting/fishing and Outdoors cuilture
Sounds like you are on the right track talkin with AirNZ and such, theres plenty of Websites regarding hunting information, its called DoC, Department of Conservation.
You can print off Permits to hunt certain Areas of Govt/Public land before you get there and a Hut ticket will cost you $6 a night/ticket... but aslong as you have a few Spare in yer pocket, and are 99% confident theres already a few tickets in the mail box, then you can get away wit ha few nights ... no real biggy
I just sorta mean are you taking a Elegant mountain rifle to leave in NZ or just a Remington 700, which could be had for $600-$800 second hand... BYO scopes and stuff. Marlins are Cheap and Tikkas are abundant.
Good stuff
WL