If you're paying rather than award then you have options. Google Flights is a good way to search and get a feel for prices and options except for the LCC airlines. Remember that you can search generally for destinations. <DFW - "New Zealand"> is a perfectly fine search term within GFlights - and it will get you some interesting options and (potentially) open up some surprising savings/availability; airline ticketing practices are sometimes quite odd. When I was flying US-NZ 4+ times a year I would often end up with tickets that were something like STL-TRG in J at 2/3 the price of DFW-AKL, but the ticket flew STL-DFW-SYD-AKL-TRG. I would either then fly from TRG to where I actually wanted to go, or just ditch the AKL-TRG part once I got to NZ. That sort of game has to be played as separate 1 way tickets, lest your return gets cancelled if you dicth the last leg incoming. *VERY* generally, booking 6-9 months out is going to be the sweet spot on cash fares from the US to NZ in my experience.

In terms of comfort, I wouldn't go near Air NZ J product, but then I dislike Air NZ in general. AA is ok. UA is nicer, generally. QF is ok. FJ is rather nice *IMO*, but I'm in the minority in liking it apparrently. There are other options, including via Hawai'i or various Asian hubs. By the time you fly there may be options on a South American carrier again, or you could go the long way via the Middle East on Emirates or similar. There are also a wide range of Low Cost Carriers that could get you to NZ in some form of J, but they will be slow and their idea of J is often .... poor. Air AsiaX, for example. It all depends on time and price and where you want to spend those.