Air New Zealand "Sweet Spot"

I'm an annual visitor to the South Pacific.

This year I'm having problems getting a reasonable (less than $900) price for LAX-Rarotonga tickets on ANZ for the Nov-Jan time frame.

Any ideas, comments?

Air New Zealand has a monopoly on that route...

Possible alternatives (fly to Papeete and from there to the Cooks, or to Auckland and the backtrack to the Cooks) are unlikely to be cheaper...

Perhaps, you'll have to confort with a flight less than 1000US$ if you are able to find one of those fares yet.

If you have enough miles you could use them this time...