Holy guacamole! I honestly can't imagine spending that much on a week of groceries... for my 7-person household (4-5 adult-sized mouths at any given time), a typical week comes in around $150, not including non-food items. I cook one family meal each day (5-6 days per week), and anyone who doesn't want that can grab something different (two of my kids usually eat little - or nothing - of what I cook). I keep a variety of foods on hand for everyone to have their own breakfasts, lunches, and snacks.
The important part here is that I don't follow someone else's meal plan -- I write my own. I check online ads for stores I'm willing to shop, and make a list of what I'm most likely to want (or what the family would enjoy) with pricing. Based on what's actually on sale, I'll work up a custom meal plan each week, pulling from recipes I've used before or "new" stuff I want to try out. Then, I use the meal plan and recipe reference to make my shopping list, separated by store so I can get the best possible value for our money.
I make my own mayo as well as most of my own dressings, dips, sauces, etc. I'll use store-bought condiments that are inexpensive, but I don't bother with the pricey ones no matter how good everyone says they taste. If I can't find it cheap or make it myself, I'll do without.
Kroger's where most of my shopping is done, using ClickList -- I order online and pay $5 to have an employee go collect everything and bring it out to my car, allowing me to avoid walking the store and potentially spending more money than I should on stuff we really don't need. We use digital coupons and paper ones, nearly always reducing the overall bill by more than the service fee, and I get FuelPoints. It works for us.
Sprouts is my favorite for produce in general, and they often have great deals on fresh meat, too. I get my coco-aminos and daikon radish there, as well as a few other things that I can't find at my other local stores.
Aldi and LIDL are my backups. I don't go to either one often, but will go if they've got enough on sale to warrant a visit. Aldi is close enough to my house that it doesn't take a lot to warrant the trip, especially when they drop the price on the 3-pack multi-colored bell peppers.
I also really like our local butcher, which has some pretty good sales at times. Unfortunately, I don't often have the funds available to run there since the better prices are on the larger packages of meat.
Ground beef is the majority of our protein, but I'm always on the lookout for good deals on chicken. Roasts have to be on a really good sale for me to bother with them, because I'm generally cooking on the 8-portion level for the sake of having at least a little left over.
...I'm noticing how long this post is, despite attempts to shorten it, so I'm going to stop now...
While meal plans are great, you may find you don't need as much variety or the shear amount of food that is offered there. The message her: simplify. Personally, I find (and recommend) that making double batches of favorites and cost effective recipes are helpful. I plan the same 1-2 breakfasts (think a frittata) and lunches all week which cuts down on the number of different ingredients I need to buy. I also started doing about half of my shopping at Aldi which is saving my family of 5 an average of $40 per week. Picking vegetables and fruits that are in season (summer is a great time to Whole30!) is a plus. If you bought condiments that can be made at home, this can save money - making your own mayo is so easy and can save you a lot of money. As you navigate this week - pay attention to how much food you are really eating vs. wasting. What meals could you simplify? Melissa is famous for her ground beef with "stuff." Making a big batch of ground beef to have in the fridge and then doctor up with veggies, an egg, dressings, etc. for meals throughout the week... you can literally Google "Melissa Hartwig ground beef and stuff" for pictures