Lets blow a few common beliefs about how fast food spoils. The results are purely ours and it could easily be longer.
Regular eggs will last over a month. Buy them in foam or paper dozens and store where they will not have anything fall on them. Paper is preferable because you can toss it overboard.
Mayonnaise - listen to the screaming when this is done -- unrefrigerated this stuff will stay good for over a month. Unless and until it is contaminated, it will grow nothing. The squeeze bottles are great because you can eliminate contamination. If you use jars, boil the spoon you use or shake it out. It will last for weeks opened and you can tell if it has outlived its usefulness because it begins to separate.
Butter - same as Mayo. We buy a tub or two on the way out and take care with contamination. There were some margarine squeeze bottles too. The tinned butter isn't hard to find in many countries. I never even looked in the states. But, it lasts forever and so a few small Tins always live on the boat.
Powdered eggs. I've tried them. they were ok. They would be good for cooking, but why if you can crack a shell instead?
The world seems a bit small to have to worry about this unless you are heading for truly remote places. For most people who stay in the tropics this will work. for those in the 30s to 50s, it is cooler to begin with and there is still a store somewhere reachable.
BTW - Moe's undergraduate degree was microbiology and she used to be a med tech. I trust her calls on this stuff. Personally, I don't know anything I didn't see.