I'm really foggy on the specifics at the USA Federal and State level, but a lot of muzzle loaders (percussion, flint, modern, traditional) aren't considered firearms in most of the USA, or at least aren't restricted to NZ citizens to purchase. You will definitely need to do your due diligence on this, but you may just be able to rock up and buy one while you're there for a hunt. There may be some limits on exporting one even though it might not be possession controlled inside the USA, and NZ would obviously want an import permit, but it's definitely a possibility worth considering.
If you have a connection there, they could get it reserved for you so you had the make/model/serial number for the NZ import permit (do that well in advance, I got jerked around last year on that and they issued me a permit the day after I came back to NZ despite being told repeatedly when I needed it for and applying well in advance). Again, I'm really fuzzy on this, but it is worth looking into.
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