I do envy your planned trip. My husband and I work on yachts based out of Ft Lauderdale so all of our time spent in the Bahamas is working. That said, I have had the displeasure of trying to provision in the islands and yes, as you get farther into the out islands the harder it gets.
As you well know, most foods people eat on sailing adventures tend to be out of cans and boxes or things that can be stored without refrigeration. I spent a month sailing on a 36' Alberg, for pleasure, through the Caribbean pre-primal and we ate a lot of rice and beans with fish if we caught any and without if we didn't. Having an unlimited supply of rum made our sad catches that much more bearable.
You won't be far from markets wherever you sail so there is always the possibility of finding some fresh (ish) veg and meat--it might even be goat. Fruit shouldn't be a problem as long as your willing to eat the fruit that grows locally. And really, isn't that part of the fun to shop the local markets and see what you can find? If you go to restaurants you'll find a lot of grilled fish and meat, but most of the side dishes, at least at most of the places the locals eat, will probably not be things you'll want to eat (mac n cheese, mac n cheese, mac n cheese), but you can usually find a salad of some sort.
If you make it to the Exumas make sure to go to Chat n Chill on Stocking Island. Get lots of conch salad and make sure you go on Sunday for the pig roast. If you're lucky they'll have some cracklins' left.
Other than that, as far as provisioning, I'd suggest to just get as much canned veg as you can and try to get the highest quality of it that you can find. Ground beef/pork/chicken can be flattened out and put in freezer bags and stacked in a corner of your freezer. Fresh eggs shouldn't be a problem to find, but might be a little pricier than you are used to. Most of the islands I've been to have had open air markets with a variety of interesting things maybe someone will be selling local eggs since there are plenty of chickens on the islands. Oh, and you won't have a problem sourcing coconuts.
Regardless, make sure to take full advantage of your 80/20 and enjoy some local specialties.