Excellent advice, Alan. I kept my boarding passes and had planned to fax them to American Airlines. Air Pacific was actually really quick about it. Within a week my account was credited for the miles.
This was my experience with Air Pacific:
The flight from LA to Nadi was very nice. I booked a few months in advance and chose row 27 which is the first row of economy in the 747-400. That way nobody reclines in front of you. There was lots of legroom. Instead of the TV on the seat in front of you , it folds like the tray table. Air Pacific didn't have any special meals (I ordered a fruit plate).
The day before my return flight, Air Pacific cancelled that one. When I showed up at the airport in Nadi 3 hours before the flight, the line was already out the door. It moved steadily, except for one family of about 12 people. They took about an hour to sort their seating arrangements. Why Air Pacific didn't deal with that separately I don't know. But for economy, they only had about 4 windows open. When it was my turn, the agent was incredibly fast. Then I looked at my boarding pass and saw that they stuck me in a middle seat in the back. He was polite to tell me that reserved seats can be changed. I asked him to politely move the people currently in row 27. He offered a compromise: sit on the upper deck. I got the very first row. Those seats are right up against the wall in the front, so less leg room.
I chose to spend a night in LA before returning to Boston. That gave me some room in case the flight was delayed. It kept me from two redeye flights in a row.
Overall, they were fine. The service was polite, and the flight attendants didn't disappear like they do on US carriers.
Air New Zealand is supposed to be good. They use older 767's with no private TVs. Same 32" seat pitch.