A better title would be, "How to sacrifice you health for money." No thanks.
I can be cheap with a lot of things, but not with the food I put into my body. The kind of diet OP proposes may work OK for a while. The younger you are, the more resilient you probably are, so that can be quite a while. But sooner or later, especially if you're a little bit older, you will be trading quality of life for a few bucks.
AFAIC, the best possible use for limited resources is excellent food. This first thing this means is fresh produce, which, frankly is difficult to find "on sale". OP's advice to eat at home is excellent, OTOH, I'd rather spend 7 bucks on a restaurant salad bar than 3 bucks for a home cooked highly processed meal.
Almost everything in life, including work, is a marathon, not a sprint. I intend to be just as strong at any point in that marathon with proper lifestyle, especially nutritional excellence. Saving $ intelligently is always smart. Sacrificing potential health and well being for a few hundred dollars per month is just not a good idea.
Pass.