Not only does PB encourage you to limit your ideas of "food" in some areas, but also encourages expansion in others. Every now and then I make beef shanks in the slow cooker- I have to very consciously take very small portions of that, as it is sooooo filling. The broth is thick and strong and it really doesn't take much to fill me up at all. Shanks and other non-standard cuts are often very cheap.
Most of the other suggestions have been pretty good so far (buy in bulk and from farmer's markets especially), but if you have the time and space, planting a garden is an awesome way to increase your food stores. Your older kids can help pick out what they want to grow, and can even be responsible for chunks of it. I'm sure there's lots of info online about how to can and/or freeze the extra for later.
Lots of: urban hiking, cycling, sprinting
Lots of: fresh meat, seafood, eggs, organs, tubers, starch fruits, vegetables, meat fat, dairy fat, oil fruits
Some: cured meat, dairy protein, sweet fruits, rice, pulses, tree nuts, oil seeds
Minimal: soy, refined proteins, sugar, liquid carbohydrate, grains, refined oils, peanuts