The Polynesian islanders were among the first people to navigate the oceans, and they used the stars to guide them. The sun marked their day, but very strict records of stars were kept in order to guide them during the night; this practice started before the dawn of the Christian era -- over 2000 years ago.
Often, the way they would keep track of stars was by creating mythologies around them, much as the Greeks did. For example, the Pleiades (an open cluster), Jupiter, and Aldebaran (a bright red star), are central to the founding story of the polynesian culture.
By using fixed locations on the horizon, sailors memorized hundreds of stars and were able to determine their longitude and latitude to a high accuracy. By memorizing the positions, brightness, colors, and time of year that stars were visible, sailors were equipped to navigate at any time during the year.
From here...
http://home.cwru.edu/~sjr16/advanced/pre20th_ancients_others.html
I took a look at Ziegler's Hawaiian Natural History, Ecology, and Evolution last night. Ziegler seems much less sure of all this than you do. He speculates that the Polynesians may have believed in a concept he calls "zenith stars" because they observed that one of the bright stars in the sky passed directy over their island, and set off using other bright stars to lead them to other islands.
This seems extremely specious to me. A "zenith star" merely marks a ring of latitude. But it does indicate to me how little is actually known about this history.
ML/NJ