Thanks for all the replies!
Found out yesterday it will likely be the end of February or March before we're able to head over - FBI results take forever! But, it does give us some more time to prepare.
I've thought about trying to get more luggage on a plane - but we don't have that many suitcases, and I'm not sure how well boxes would stand up to being moved around that much... we also won't have room to store extra suitcases in our place over there.
We're flying out of San Francisco - we've found a flight that only makes a stop in Auckland, so that helps a ton! Also, we don't have a place lined up over there - we're going to try to find a hostel or something similar to stay in for cheap while we check some places out, so not sure how it will all work with luggage coming over....
So much to think about!