Anthropologist of South Pacific foodways here.

Hawaii is not my specialty (it is more around Micronesia and the general area of French Polynesia and similar islands), but I feel qualified to answer this as I know a little about Hawaiian foodways and many South Pacific traditional staple foods and agriculture are similar.

First off, I will break this down into two categories, carbohydrates and proteins.

Carbohydrates in traditional diets make up the bulk of caloric intake for South Pacific populations. This is principally in the form of root crops, breadfruit, and bananas, with the cultural and caloric importance of each varying between islands and cultural groups.

Now I don't know if in Hawaii those three varieties of permissible bananas for women were important to their diet, but even if they were not there exists plenty of other sources of carbohydrates.

Indeed, taro is a root crop and in many South Pacific cultures the preferred food, but several other types of root crops were cultivated as staples. Among these:

• Three species of yams in Polynesia, with more existing in other parts of the South Pacific, only one of which was a major staple (Dioscorea alata) while the other two more or less famine foods consumed in harsh times.
• Sweet potato, introduced to the region hundreds of years before European contact, I do happen to know Hawaii was one of the islands which integrated this crop the most in its diet and agricultural system as a veritably important source of food
• Giant taro, a historically important root crop cultivated in large swathes over the South Pacific, including in Hawaii. Needs to be cooked or processed thoroughly as it contains many raphides (much more than taro), but historically as been one of the principal sources of calories in the South Pacific. In some islands, though none Polynesian I am aware of, it is even preferred over taro.
• Giant swamp taro, similar function of the giant taro, generally the traditional staple root crop of South Pacific atolls as it grows well in the somewhat brackish and marshy freshwater lens aquifers of atolls. As far as I know this was not important in Hawaii, if it was cultivated at all.
• Malanga (cocoyam) and Sweet cassava, which can be consumed as the root without the extraction process bitter cassavas require, were introduced post European contact.

Keep in mind that all these crops were cultivated in many different varieties and thus with only one species but various varieties you can have access to a large array of nutritional profiles, with for instance one variety rich in vitamin A and another in antioxidant.

It is also fundamental to not forget nor underestimate the breadfruit. This tree exists as well in countless of varieties all over the South Pacific, and was an immensely important staple food and source of calories and nutrition in huge parts of the region, including Hawaii. The volume of food produced by breadfruits is impressive, and it literally grows on trees. It is literally a giant crop of starch that grows in huge balls on trees as fruits. It is seasonal, but several methods of breadfruit preservation exist, and in many islands the breadfruit season is recognised as the season of abundance and when people eat very much and grow fatter (to clarify, this is seen as a positive thing), whilst in opposition the other part of the year is seen more as a lean season where more work is required to produce less food. Generally speaking, there exists two breadfruit seasons, a major and a minor one. Do not underestimate the breadfruit my friends. I am sure my fellow Caribbeans will also agree with me we also share an enthusiasm for this wonderful tree along with our friends from another ocean on the other side of the world.

And now for the proteins, which pre-European-contact in Polynesia consisted of four sources:

• Pork, which as established was not permitted for consumption by women, in reality was in the whole of the region a feast meal and display of wealth, power, and celebration. Indeed at feasts large quantities of pork were eaten, but it was not an everyday meal and therefore not the principal source of protein.
• Chicken, which were an occasional source of protein but like pork not everyday, although it does not hold a symbolic importance akin to pork.
• Maritime sources of protein as the most important. You say several types of fishes were prohibited for women, but the varieties and abundance of food collected in South Pacific maritime systems is enormous. Not only fishes (which many species could be consumed by Hawaiian women without breaking taboos, but also species such as several types of molluscs which were consumed in large quantities).
• And finally, hunting terrestrial and semi-terrestrial animals, ranging from land crabs to coconut crabs to multiple birds (which in many islands depending on epochs seemed to have been particularly important in South Pacific diets).

Vegetal protein as you can see can be considered for all practical purposes not present in the traditional diets, especially as traditional systems of agriculture did not utilise many legumes, and when they did they provided more carbohydrates than proteins (as in the the case the Polynesian chestnut trees).

Fats and other sources of nutrition also were consumed usually in vegetal form, of course an important source being coconuts which Hawaiian women would not have been able to consume, but also using crops such as candlenuts (the famous Hawaiian kui-kui).

Fruits such as Pandanus and noni, among others, would have provided other sources of nutrition, both raw and processed (pandanus paste or noni juice for instance).

Finally, I use a lot of past tense in this response, and I want to clarify it is not because I wish to position Polynesians or other Pacific people are pertaining to the past, but uniquely because I am talking about pre-contact agricultural systems and foodways.

EDIT: Wooo many questions, I will answer them but it is late where I am right now and I am waking up at 4am and will be all day in rural valleys without signal or free time for my work, so I will try to answer all of them tomorrow night but likely I will come back very very late so most likely I will answer them Friday when I have time.