I don't know if this will help, but it's just my 2 cents...... Our food bill wasn't nearly as high as yours, but like you, we were looking to cut where we can.
So, I do make up a "menu" for the month and base our food shopping lists on the menus. ( I try to food shop once every 2 weeks.....then go to the store if we need milk, fresh veggies)
But I really found that it helped me stay focused and not "impulse" buy. The other thing I learned how to do is to stock up when something IS on sale. For example, we have Kroger here...so every once in a blue moon they'll do a stock up sale. Well, Classico spaghetti sauce was $1.49 (ea) when you buy
8. well, that's the brand we use, so I actually bought 24.

My DH thought I lost my mind. Normally though, they are $ 2.89 each, so I saved $33 on something we use anyway. BUT, I don't have to buy that for a REALLY good long while. Same w/ pasta .
We bought a 4 tier shelf unit from Lowe's and put it in the laundry room. Now when something goes on sale good, ( and we actually use that item) I'll buy it in bulk and put it in there. I've found that it saves us a tremendous amount of money. This goes for meat too. Hamburger will sometimes go on sale for $ 1.99 / lb. So I'll stock up....then plan meals around that... spaghetti and meatballs, taco night ( a huge hit in our house), hamburgers, etc. Or chicken....you can never have too much of that.
And, my food shopping budget has not gone up from $ 125 / week for me, DH and DD (4). I have learned to become a "smart shopper" instead of a food shopper.

I used to buy "what we need" now I try to plan around "what we have". I used to be one of those people that shopped and cooked by "well, I feel like having this "..... now I keep a list of dinner ideas so when I make up the menu, I can switch it up and we have really good healthy options.
Also, if you have CVS, learn how to shop at CVS. There's a fantastic thread on the budget board for CVS on the current sales and extra care bucks, etc. I can't even tell you how much the ladies on that thread have saved me money. They're genuine professionals !!

But really, once you start CVS'ing, it'll save you a ton on your beauty products.
Sorry this is SOOO long !!!!