you know, if i were to do this primal, i would probably prep myself rather than rely on modern grocery stores.
the most simple solution would be to make and utilize pemmican, which can keep quite well in cool temperatures for a number of months. even so, i would vacuum seal it into proper sealing bags so that it may keep even longer.
here is a recipe for making traditional pemmican. this is essentially dried meat and rendered fat, similar to a sausage, and then tightly packed into a cake. it is highly dense and nutritious, particularly suited to this sort of travel.
in addition, i would make jerky, determine daily amounts for that, and then seal it in it's own pouch.
next, i would ferment veggies in all sorts of forms -- krauts, kim chee, salsas, various cole slaws that i also like to ferment, etc. a daily veg, so to speak. i would make them into servings of my daily amounts, and vacuum-seal them.
after this, i would dehydrate some fruit leathers of various sorts. then i would vacuum-seal them into daily pouches.
i would also carry nuts and dark chocolate. i would also carry tea, because i'm obsessed with drinking tea.
i would make enough for every day of four months -- which would come to 120-130 days worth. I would pre-box each package for my friends to send to the post offices were i'd be picking them up, so that there's no guesswork. This would be 3-4 pouches for each day (pemmican, jerky, veggies, fruit leather).
the reason i would vacuum seal the pouches is two-fold: 1. better keeping; and 2. less air/density/weight to carry. all of these things, actually, can be fairly easy to carry -- and the fermented veggies, you won't need a whole lot of them, perhaps about 1/4 cup per day or so. this is mostly for digestive aid and added vitamins. so, everything becomes small and nutrient dense and easy to eat and easy to carry over so many days. Also, you won't need to cook a thing. you can just cut open your pouches for the day at your meal time, and then eat as you need to.
this is probably how i would do it, personally. i think if you make 5 different flavors of each thing (eg, 5 pemmicans; 5 different jerkies; 5 different ferments; 5 different leathers), then you'll be able to choose flavor profiles and won't loose your noodle about eating the same things over and over. I would probably match up my flavor blends pretty specifically, because i'm crazy like that. things have to go together for me.
when you are close to towns, might be a good idea to go ahead and hit a grocer for some fresh fruit and veg, but you probably won't need it.
when yuo finish, you have to tell us your trail name.
i've only hiked portions of the trail at a time, usually staying with people along the trail, or in huts, rather than any camping. i usually carry enough food for the day (nuts, fruit, chocolate), but would be given breakfast and dinner by these friends or hosts.