You can probably bring some fresh carbs (like bread) on the hike in, plus some gatorade or other electrolyte containing substance to stay hydrated. Don't know if there's a bakery like Tex's on the big island to grab some malasadas (filled donuts, . filled with healthy stuff, of course)….
After arrival, 3 weeks on the same stretch of beach, so it sounds to me your situation is more a basecamp requiring a variety of different foods (example: a different protein and starch combo every night, different breakfasts every morning) – thus I will need to defer to the cookmeisters on the forum. I do not see how to avoid dehydrated or prepackaged freeze dried meals for 3 weeks living out of a pack, though. Even fishing would get old to this fresh fish-lover (Hawaii and California are my favorite trips for this reason).
If it were me, I'd do things like a few Italian dehydrated meals (a few spaghetti and meat sauce, a few angel hair and pesto), a few American meals (beef stew), a few clam chowders (dehydrated again) when the north storms hit the beach, some Tex-Mex rice n'beans type combos, etc…… heck, even some glammed up typical backpacker fare like ramen with egg powder dropped in like egg drop soup … I'm going to need to eat lunch soon. Speaking of soups, once adjusted the nights will seem a little cool and can be wet, so maybe a different soup mix for every night? You may have to plan your meals like a space mission. Just have enough food to hike out!!!
In terms of barter, anything but fish. Fish is pretty inexpensive in Hawaii, so typical American fare may be the best option as this is at a premium (either imported or grown on the island for tourists). Hog is always "in season" but in some areas are hunted out. I've only gone in for a few nights at a time so canisters worked for me. White gas with a campfire backup sounds fine.