We usually arrive a day ahead also - occasionally 2 if we can't work the air out the right way.

I guess it also depends on where the ship's next stop is. The cruise that the OP mentions goes from LAX to SYD so next stop could be Hawaii or somewhere in the Pacific (a few days later as well as could be difficult to get to - so perhaps more leeway is needed). If it's something like a Caribbean cruise leaving from FLL or MIA with the next stop in Key West - maybe don't worry about it - since you can probably get there quite easily (relatively) if you "miss the boat".