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I also have Goodwillie ancestors from Fife in Scotland but haven’t quite managed a connection to the New Zealand crew, but I’m sure it’s there. I have the following snippets of information which may be of use.

There was a Charles Goodwillie, an engineer from Strathmiglo in Fife who went to New Zealand about 1838 and married Kura on Stewart Island in 1844. In 1851 he was presumed dead.
Charles and Kura had two children:
(1)   Charles who had 12 children (Caroline, Charles, Mary, John, Catharine, Jane, Charlotte, Rachael, Albert, George, Thomas, Marion).
(2)   Charlotte who married John Davidson

I also have a note of a Charles Goodwillie who was born early 1800's and married Ngai Tahu Maori Kaumatua. Not sure if this is the same person.

Also the following from Riverton Cemetery, Southland Province, New Zealand:

Goodwillie, Caroline (Hunt), d. 25 Dec. 1907, age: 66yr, Beloved w/o Charles Goodwillie, s/w Marion and Thomas, [PA]
Goodwillie, Charles, d. 2 Dec 1930, age: 90yr, s/w Caroline, s/o Caroline & Charles Goodwillie, [PA]
Goodwillie, Marion, d. 17 Jun 1898, age: 16yr, s/w Caroline, d/o Caroline & Charles Goodwillie, [PA]
Goodwillie, Thomas Edward, d. 1 Nov 1906, age: 29yr, s/w Caroline Goodwillie age different in family records, [PA]

Good Luck!