In the United States we've come to believe that just about everything needs to be refrigerated. Those of you from Europe or Asia certainly know better, as do blue water sailors.
Does butter need to be refrigerated? Of course not. Cheese? No, absolutely not. If you're going to be gone for a while, wrap a bit of cheesecloth around that block of cheddar and moisten it with vinegar. Worst case scenario: you'll have to trim off a bit of mold now and again, but not likely if you use the vinegar method. Of course, if you insist on overlanding with camembert, it may get a tad runny.
Farm-fresh eggs: get them BEFORE they've ever been refrigerated and coat each one with petroleum jelly. Room-temp storage is fine for up to three months. Heck, my grandparents and great-grandparents used to put up crocks of fresh eggs in waterglass and store them in the cellar; they were good for years.
Cabbage? Just peel the funky leaves off and it's nice and fresh. Whole salamis, onions, potatoes, garlic, carrots, peppers, fruit, even asparagus...sailors swing them in a little hammock to allow air to circulate and they last a long time. Of course, dried herbs will be more portable than fresh. Visit a good Asian market to find an astonishing variety of dried herbs, spices, fruit & veggies, and a wide range of protein sources.
Larry and Lin Pardey are well-known sailors who have written extensively on cruising life with minimal power requirements. They have written
an authoritative text on cooking far from civilization that has direct applicability to overland adventurers.