I did find this discussion about traditional farming in Hawaii, but it only discusses the land division system.
http://cms.kohoia.org/course/v...
This article describes culture history from the perspective of three archaeological sites on the west coast.
http://www.donch.com/LULH/cult...
In this section the authors do mention the importance of slash and burn [swidden],
Quote: Several other dry land crops were also important food items. They were cultivated by means of swiddening — clearing vegetation by cutting and burning, followed by alternate periods of planting and leaving the land fallow. Sweet potatoes comprised the main crop where insufficient water occurred to grow taro. Breadfruit trees were planted in groves in sheltered areas with fertile soil and little wind. Numerous varieties of bananas grew in clumps around taro patches and in gulches. Yams were raised to some extent in the early days, but because of their mealy texture were not a favorite food. Later they were grown to sell to sea captains because they spoiled less quickly than taro or sweet potatoes. Other vegetables in the Hawaiian diet included coconuts, sugarcane, arrowroot, and seaweeds. Other plants extensively cultivated were the paper mulberry for manufacturing barkcloth (kapa), the 'awa for use as a narcotic, bottle gourds used for containers and musical instruments, screwpine (pandanus) used in making mats, and a variety of other useful plants. End Quote.
The pond farms (aquaculture) are also interesting.