FYI those AirNZ rules are for international flights. Domestic is easy, rock up with the firearms in a locked case, and ammo and bolt in another locked bag, sign the docket and produce the docket when picking up the bags. The downside is that you need to have 2 bags on your ticket, and make sure you do it before arriving at the airport. $30 extra when booking the ticket vs $70 when paying at check in.
Flew Jetstar only once in 2012 with firearms and the check in folks had to call thru to Australia for information on firearms, it just wasn't worth the hassle.
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On the plus side of travelling with firearms out of Queenstown, the security / x-ray folks are very chatty and let you take photos of your gear when it's xrayed.