For stoveless options, the potato flakes mentioned above work with just a few minutes soaking in cold water. Ramen noodles are already fried and can be eaten out of the package like a large cracker, or soaked for a while in cold water. Instant bean flakes are difficult to find on the road, but they work well with about 20 minutes of soaking. Rolled oats are cooked during processing and can be eaten out of the box or with a few minutes of soaking.
My staple while hiking or cycling is a muesli I make on the road out of rolled oats, lots of walnuts, and raisins. I eat a cup, with cold water, several times a day. I can find those ingredients in almost any store in the US and mix them in a ziplock bag. I used to add powdered milk but I find it just as tasty with plain water.
I'm not a huge fan of peanut butter, and I usually try to stock up on tree nuts instead. I can almost always find cashews, almonds and walnuts in US grocery stores. Walnuts for some reason are cheaper in the baking aisle. I'll buy a jar of PB every week or so for an extra boost of fat and salt, but it's not my favorite.
I always eat some raw veg every day, even if it's just a few stalks of celery or some carrots or a pepper. I never pass up fresh fruit. I love touring during local harvest season, when fresh stuff is literally falling off trucks. I try to convince myself that the minute amount of fresh food I consume is somehow making up for all the processed crap I'm eating on tour.
I'm not as strictly vegan as you are and will sometimes carry cheese, especially in dairy-producing regions with small farms and you get the really good stuff. I'll eat an egg dish at diners sometimes.
My last two-month tour also cost US$7 per day in food. That's also the average I spend on long (up to five month) trekking trips. That does not include town meals eaten while resupplying and that's a different story. Thanks for the breakdown by food type--I haven't looked at it that way before.