Three countries later...

We got on the Dec 29 flight to LA, a tight-as-sardines excursion that landed at LAX on time. We still came very, very close to missing our next connection as we changed terminals and went through security. With seconds to spare (the ticket agent was literally shutting down the flight as we arrived at the gate) we got on board our Air Pacific 747, en route to Fiji at last. The flight was long, but not unbearable, and the staff of Air Pacific were wonderful. I'd definitely fly with them again.
We landed in Fiji on Dec 31. Our luggage, however, hadn't made the same sprint between planes and was reportedly still in LA. No worries, though, as we had been warned this might happen and had packed our toothbrushes and bathing suits in our carry-on bags.
Fiji is a beautiful country, and the people are incredibly friendly. We went shopping in Latoka, the second largest town on the island, and spent all afternoon replying to strangers who greeted us with a friendly Bula. (it means hello. That and vinaka, or thank-you, sums up my knowlege of Fijian.)
The new year's eve party was a bit of a bust, as we all fell asleep by about 10, but we toasted the new year on Canadian time the next afternoon.
After 28 hours in Fiji, we collected our bags (5 of the 6 missing suitcases showed up on the next flight from LA; the sixth is still MIA), bought a bottle of Bounty rum at the duty free, and hopped on yet another plane. Next stop, Sydney.