So, there is a lot going on in this post, but it seems the heart of the question is not so much Cook but the creation of national myths.

To understand some of the elements of this instance, I have a bit of reading to suggest which might help shed some light.

• Gananath Obeyesekere, The Apotheosis of Captain Cook; European Mythmaking in the Pacific. Princeton, New Jersey: Princeton University Press, 1997.

The cat-fight that is going on in this book (and others) between Obetesekere and Marshal Sahlins is not what is important to find in this text. Rather, what it might help highlight is the ways in which, immediately after Cook's death, he became a mythic fallen figure, a hero to Enlightenment ideals. The 'bad history' over Cook's life & death in a larger sense begin there (or, you could probably say it begins as soon as he leaves port the first time and John Hawkesworth is hired to edit the journals and logs for publication when the ship returns).

• Michel-Rolph Trouillot. Silencing the Past; Power and the Production of History. Boston: Beacon Press, 1995.

This whole book might be on interest, but I think you may find chapter 3 on Christopher Columbus to be particularly salient to the ways in which mythology making operates-- especially foundational mythologies of settler societies. Historical figures make for easy appropriation in the present-- but that does not mean that there is not typically a reason or logic behind doing so. Colombus, even though he never made it to the US, became an important founding figure for immigrant communities-- especially Italian-Americans (or Catholics at large) who could stake their own claim against cries that they did not belong in the US by holding up Colombus as proof that they did. Cook can operate in a similar way because Australia is/was a British settler colony, he was the logical founding figure, not the Spanish, Dutch, or French that also stopped by.

• Moorehead, Alan. The Fatal Impact: An Account of the Invasion of the South Pacific, 1767-1840. Honolulu: Tales of the Pacific, 1966.

Moorehead was not a historian, yet his 1966 book Fatal Impact has had a huge impact on Pacific History. Moorehead takes what I believe you might peg as the left wing approach to this history. Rather than Cook as triumphal figure, Cook is the one who opens Pandora's box. In each of his sections (or case studies a historian might would say) Moorehead moves from the descriptions of Cook to further intrusion by westerners; missionaries in Tahiti, convicts in Australia, and whalers in the Antarctic. The effects of these new arrivals is the displacement of the islanders, a biotic revolution, and radical shifts in culture. Moorehead illustrates the ways in which the preexisting cultures could not continue in the face of western land appropriation and industry, literally squeezed out in some cases. He draws a straight line between Cook and what comes next-- which is not terribly controversial as Cook's logs did inspire many more returns to the Pacific by groups less interested in exploration or Enlightenment. The more controversial part of the book is the depictions of the islanders as simple & happy and then corrupted-- or the idea that European contact was 'Fatal' to Pacific societies and cultures.

• Beaglehole, J. C. The Exploration of the Pacific. Stanford, California: Stanford Univeristy Press, 1966.

Beaglehold is the Cook biographer par excellence. He was the Cook expert during his life and his books border on being hagiographies (celebrated biography of a saint). It does give a good idea of the standard sort of history of Cook being written during much of the 20th century as a master navigator who met an untimely death. The books are relatively celebratory and include accomplishments and success without much questioning of how the voyages connect to the larger history before and after.

*Smith, Bernard. European Vision and the South Pacific. Melbourne: Oxford University Press, 1989.

• Smith, Bernard. Imagining the Pacific: In the Wake of the Cook Voyages. New Haven: Yale University Press, 1992.

Both of these Smith books also contain a great deal about the reception of Cook and his voyages back in Europe and help explain the prominent position he held upon his death. Again, while these images are important for understanding Cook's position as a fallen figure of the Enlightenment, they were carried back out into the Pacific by settlers in the late 18th century and after. Cook was the noble figure of sacrifice as they saw it.

• Eric Hobsbawm and Terence Ranger ed., The Invention of Tradition (New York: Cambridge University Press, 1983).

• Anderson, Benedict. Imagined Communities; Reflections on the Origin and Spread of Nationalism. New York: Verso, 2006.

These last two do not directly pertain to the Pacific, but they do relate to the creation of national mythologies. Hobsbawm & Ranger's collection is a classic and it does a lot to provide other examples of figures who became subjects of 'bad history' or maybe we should say national histories. I am thinking mostly of Chapter 3 by Pros Morgan on Welsh hero/myths as focal points for the formulation of a modern Welsh identity. Or, the final chapter on mass produced traditions-- which leads into Anderson's work-- on how figures or practices such as Cook or Australia Day-- play a role in the creation of national identities and allow us to imagine that we are part of some larger national project along with thousands or millions of other people we have never and will never meet. Cook serves as a focal point in this regard because everyone imagines that everyone else has heard or learned the same stories when they were in school and its just a few (left or right wingers depending on one's perspective) who have distorted or 'rewritten' the tale. He is part of a shared 'genealogy' of (white) Australians.

One place that would be really fruitful to study the evolution of Cook's place in Austalia's national mythology is through either public school history textbooks across the decades to see how discussion of Cook has changed over time, or, public government speeches commemorating his coming (on the occasion of anniversaries or dedication of statues) which may or may not be recorded in local newspapers.