Congrats Clark, you are going to love it there. Learn to fish in the surf and you can still pull in some nice catches in Kauai, not so much on Oahu which is overfished. The way to live frugally in Hawaii is to buy the stuff that is cheap. That seems obvious, but what I saw a lot of people doing is trying to live the same way as they did on the mainland. That's why people think it's expensive. They also freak out when they see milk at $10 a gallon. So, skip the dairy and eat more mangoes and you'll be fine.
Expensive
Blueberries and apples
Grocery Store Chicken - it's all imported. But, tons of feral chickens and supposedly you can trap them without too much trouble. Especially in Kauai where the chickens outnumber people.
Dairy, there is one dairy in Oahu but very small. This means cheese, yogurt, butter, etc.
Atlantic seafood (Lobster, Cusk, Cod)
Cheap
All kinds of Pacific fish and seafood. Sashimi grade tuna for $4-5 a pound in the grocery store. Blue Marlin. Oh, I miss this the most about Hawaii.
Poke - I ate this 2-3x a week, endless variety
Mangoes, apple bananas, papaya, sometimes pineapple (many are imported now from the Philippines)
Taro - I enjoyed poi but it really makes a big difference where you get it. Taro chips and bread was good, too, and cheap.
Beef - there are several herds on the big island and one on Oahu.
Pork
Lettuce and greens (12 month growing season)
Electricity is expensive, and fuel is all imported and tends to be more expensive. Solar is very popular and makes a ton of sense there (very close to equator so makes electricity efficiently 12 months of the year). There is a VAT tax on everything, which is how the islands run efficiently, they get a ton of tax money from the military and tourist populations. Look for Kama'aina (local) prices, which are available almost everywhere if you ask for them.
I do sometimes wonder about feeling cramped there, and no seasons.
I never experienced Island Fever, but some mainland folks had trouble with it. The Big Island is pretty big, so if this is a concern, that's a good place to plan to go. The islands do experience seasons. It's somewhat subtle, but there is a rainy season (Winter) when the big waves come to town and a dry season (Summer).