Peter, flying in a day early is of course the perfect solution. I see no problem with the return at all. You might consider purchasing your transfer from Royal Caribbean; but even if you don't, you should be off the ship by 10:00 and at LAX before 12:00. Have a wonderful trip!
By the way, I did a "pub crawl". among other things, in your fair city while on a Princess cruise from Auckland to Sydney a few years ago; I absolutely love New Zealand and the people are the warmest and friendliest I've met anywhere. God bless.