Success! I finally found someone in Denver who knew that this wasn't correct, and it is straightened out and ticketed. Apparently the 80K rule applies ONLY if you change flights in Oceania on the way to NZ. Since this flight stops and then continues on the 60K is the correct fare.

I really might have given up had it not been to you guys encouraging me to fight this. Thanks so much. You've saved us 40,000 miles.