Your kitchen appliances should be your friend, NOT your enemy. If you know how to cook you could make large batches of food that could be stored away for later use by either vacuum-packed freezer bags or home canning. Not only do you get far fresher food, but also you skip out on a lot of the chemicals in store-bought food that can occasionally cause no end of problems in children. Maybe the Mormons--with their strong emphasis on home canning--have the right idea?
My aunt does just that. No processed food in their home ever. And by the way, they grow many of their own vegetables, that too in Connecticut, of all places!