Another way & I consider even better break in your trip to Auckland NZ.Agree with suggestion to make the Cook Islands your stopover en route. It is our favourite stopover. If you have time, Aitutaki is well worth a side trip. With stopovers, the journey becomes part of the trip.
Depart LAX only on a Saturday after 11pm on Air NZ to Raratonga - Cook Islands.
It is only a 10 hr. flight & you arrive around dawn into a beautiful tropical island.
The locals are much friendlier that the Tahitians & they use NZ currency & you will not pay Tahiti prices.
Then daily flights onwards to Auckland.
Note : when onboard Noordam - do not complain to Aussies & Kiwis about your long trans Pacific flight - or you will be ear-bashed on how many flying hours from NZ & Aust. to UK.
Agree with suggestion to not overnight in LAX. We used to, but stopped once going through US Customs became a nightmare! You need a minimum of three nights for a stopover anywhere to be a relaxing break.
Hurtigruten - Fram - 2014 - Ushuaia to Antarctica, via Falkland Islands and South Georgia Islands.
Princess - Ocean Princess - 2013 - Dover to Iceland and Norway, via Shetland and Faroe Islands.
Princess - Ocean Princess - 2012 - Singapore to Sydney
Fred Olsen Black Watch - 2012 - The Baltic, with Norway. Dover to St. Petersburg, via Kiel Canal.
Celebrity Century - 2011 - Auckland to Sydney
CTMA Vacancier - 2011 - Montreal to Magdalen Islands. Amtrak - Toronto to New York
MSC - Poesia - 2010 - Kiel, Germany to NY. Amtrak NY to Niagara Falls, VIA Rail Toronto to Vancouver
MSC - Lirica - 2008 - Genoa, Italy to Fort Lauderdale
Royal Caribbean - Rhapsody of the Seas - 2007 - Honolulu to Sydney
Rivers of Holland Cruise - 2003 - to Amsterdam
Alaskan Marine Highway - 2003 - to most Alaskan ports of call
Star Cruises - Superstar Leo - 2003 - Sydney to Darwin
Norwegian Coastal Voyage - Naruik - 2002 - Bergen to Kirkenes
Angelina Lauro - 1971 - Sydney to Perth. Indian Pacific - Perth to Sydney (Put me off cruising for 30 years!)
P & O - Chusan - 1970 - London to Brisbane, via Africa, India and Sri Lanka (Suez closed).
Chandris Lines - Queen Frederica - 1969 - Sydney to London, via Panama, New York and Rotterdam