Flying via the US, though, means that you have to enter the US, in immigration terms. This is a huge nuisance for people who require a visa, and a major irritation on the trip for all non-US passengers: if you're on a flight that lasts some 24 hours and you have a two-hour stopover somewhere, you don't really want to spend it standing in a queue so that you can tell an immigration officer that you're going to be in the country for 20 minutes.

How about Singapore Airlines (SQ), who fly direct from Singapore to Christchurch?