As a bit of an update, I finally got to give this a try and IT WORKED! Verizon mini running on AT&T $25 1GB plan. Didn't need to hit the New Zealand site for a APN, it "just worked" as soon as I subbed in the AT&T SIM card. 4G is fast enough for my needs.
Again, thanks to those who showed the way! I'll probably have year-round cellular now for only $100/yr.
Even better is year round cellular for free with the T-mobile 200MB/month free plan. Activated it with no problem on my Verizon iPad mini.