I am not sure if other supermarkets do it or not BUT my Kroger routinely marks down packaged produce items every single morning. The cut up brocolli, lettuce mixes, bags of spinach, etc. have sale stickers most mornings. They are substantial markdowns too--perhaps the spinach bag is $2.69 or so--they are usually marked $1.29 or so. Perhaps you could inquire at your own market.
I am not a big meat eater but I know the meat dept. at my Kroger does markdowns each morning too--as does (GULP) bakery.
Also, have you ever considered "bulking" your recipes--putting fresh veggies into ground turkey or chicken. Thus, lowering cost.
Not a novel idea at all--but I buy when the sales are on. Sure, it's my preference to have everything fresh but when I come on a good deal I buy and I buy big.
It's been mentioned before but the bulk bins are also my friend. There is nothing in them I cannot use in some way. Some of the items are rock bottom as compared to packaged products--quinoa, millet, brown rice, cous cous, raw almonds, rolled oats, steel cut oats, etc.
"Be who you are, say what you feel. Those who matter, don't mind. Those who mind, don't matter." --Dr. Seuss