I am not sure if Air New Zealand offer F, but I have heard that trans Pacific in J they are very good, and cheaper than QF. You have to route through NZ though. They might provide the "something special" you are looking for however.
I really do not think you will find 5 return F tickets for $30K, whichever airline you look at. Certainly not on QF, even on sale.
If you were prepared to fly MEL - AKL - PPT - LAX on Air Tahiti Nui you might get cheap F at least part of the way, but TN F is less good than QF J and they don't always offer it.
You could also check whether Air Pacific offers F - you would have to route through Fiji to LAX. In J they are almost as good as QF domestic J so I would not get too excited about Air Pacific even if they do offer F.
The other possibility that hasn't been mentioned is JAL - you would have to route through Japan to LAX. I presume they would offer F between Japan and USA although I have no idea of price.
