Well I thought I had them all but....I have found another son. I had come across a couple of entries in Papers Past where Anne was traveling around the country with more children than I had accounted for. I kept searching records both birth and death thinking maybe there had been an infant that had died young.
Then I noticed that there was a John James Austen buried at Waikumete not only was his occupation listed as "seaman" but he is buried quite close to Captain John and Anne's plot. I doubled checked the Austins and found him.
John James Austen was born on the 17th March 1861 in Auckland. He was registered as John Austin by his grandmother Hannah Wilcox. I assume that Hannah could not read or write as she "signed" the form with a cross as her "mark". Perhaps that is why the name was spelled wrong.
John James died at age 37 on the 24th November 1898. So he died before Captain John.
The next bit of sleuthing will be to see if he married and had any family.