I think you need to redo your math to exclude all the non-food items to see exactly what you are spending on for food in a week. Not only will this help you figure out how much you are actually eating, but it'll help you figure out what else you are buying. This may help you figure out if you need to reduce or cut other things out.
By the numbers:
I haven't done a budget since I moved, but when I was living in the US Midwest, I was generally able to spend $40-$100 USD a week on myself and still be full. The higher totals included lots of meat.
You might wonder how I was able to spend as little as $40. Well, I bought a ton of frozen meals: the really, really cheap ones. I'm talking $1 to $1.50 per meal, and most of the time I'd eat two of them for lunch. Yes, I eat about 2 to 3 times as much as the "standard serving size" and I was able to survive, and even be full and overweight, on $40 a week. They didn't taste the greatest, but they were food.
I also got soups that were $1 to $2 a can. Tuna is cheap at less than $1 a can. Eggs are also cheap, even though they sound "expensive" at $2 a dozen. You realize that means they are about $0.17 each, right? You can get real full real fast eating eggs, and because it's protein, you'll stay full longer. Rice and egg noodles are also inexpensive and tend to fill you up easily.
The cheap end of frozen pizza that's not a "single serving" pizza was around $2.50. You could definitely get other pizzas for $5-$10, but I kept to the cheap ones. And I only ate one a week. You could sometimes get them on sale for "5 for $10". I'd usually add toppings, since they were pretty scarce out of the box, but that was less expensive than buying them fully loaded.
BTW, I'm an active male at 5'10" tall and roughly 285 lbs., so I'm not a tiny person assuming my food intake will work for everyone. In fact, I'm pretty sure I eat more than most people, as I've seen at lunch time in the various places I've worked.
Meat in the Midwest is usually less expensive than other places, since the animals, rendering, etc, is generally done fairly locally. Most of it is done within 100 miles from the retail sales, even for the "big box" stores. Nearly everything, except for fish, is generally butchered within 24 hours, so it's also fresher, but that's beside the point.
Even 2 years ago, you could get a pound of 85% ground beef for around $2.50. Pork and chicken were generally less than $2 a pound. Prepared bratwurst is generally cheap and easy to fix. Even in the larger US city (in the middle of a desert) I'm in right now, I was able to get a 10 pack of brats for $10 last week.
As for spending $100, I was able to buy a bunch of meat. I'd put it on a (large) charcoal grill all at once, then throw it in the fridge or freezer for the rest of the week. I'd have burgers, brats, chicken, pork chops, even a cheap steak, and some other things. I'd even get veggies for stir fry, chop them up, throw them in a stainless steel bowl (with a packet of spices), cover it with foil, and let those cook on the grill while the meat was cooking. By cooking larger amounts at once, you are using less energy (and the materials it comes from) to cook the food, when you consider the amount of combustibles or electricity it takes to heat up and cool down the utensils, pans, etc. It also takes less time to cook it all at once than it does to cook things individually.
I've lived in a poverty level situation for most of the past decade, so I know that it's easily possible to be full while eating less than $2 per meal. When I was unemployed, I found ways to eat for less than $1 a meal. I also appreciate eating a $4 lunch and $8 supper. I'd "splurge" once a week going to a fast food restaurant.
Yes, there were times when I spent more than $100 a week. That usually included longer use items that I ran out of. Things like paper towels, toilet paper, dish soap, and other low-use high-quantity-purchase items. Or I'd be stocking up on 5-10 pizzas for variety, which, again, I'd only eat one a week.
The last time I went to the grocery store, I think I spent $170, but that was for about 2 weeks worth of food and included quite a bit of meat. I should be able to buy only the perishable foods I use on a regular basis the next time I go and spend considerably less.
What you might also want to look at is your drinking habits, and I'm not even talking about alcohol. (But yes, alcohol is expensive, so don't drink it if you're worried about cost.) Instead of going with bottled water, pop/soda, and sports drinks, stick to tap water. You can get a filter pitcher for a weeks worth of bottled drinks and those filters will easily last you months, each. If you don't like the taste of even filtered water, well, you're going to have to get used to it. There are different inexpensive things to add to it, but even that cost can add up quickly.
You also state that you drink a lot of instant coffee. Well, you're going to have to reduce that, too. Because it has caffeine, like pop/soda, you'll have to reduce your intake slowly, or you'll likely have withdrawal symptoms. Somewhere between 15 and 20 years ago, I dropped my pop/soda intake from around 6 cans/bottles a day down to 1. I haven't regretted that decision. (I know people who drink more than 6 a day.) I've also tried to remove my pop/soda intake completely, but it's hard to do and because I drink it in the morning to kickstart the day, I found mornings miserable.
Start by determining your "normal" daily intake over a week, then immediately reduce it by 1 the following week and replace it with tap or filtered tap water. If you drink 6 cans/bottles (or coffees) a day like I used to, drop it to 5 a day. Then every month reduce it by 1 again until you either aren't drinking any of it; or you just can't reduce it any further while remaining human. Eventually your body will get used to the reduced amounts, which is why I suggest slowly removing the caffeine and sugar. If you can manage it without becoming Mr(s). Hyde, reduce your intake even faster. I managed to drop from +6 cans a day to 1 without any problems, but I was also still fairly young, in better shape, and had more discipline and determination than I do now. YMMV.
Caveat: I still drink more than 1 sugary or caffeine drink a day if I'm doing a lot of physical labor. I normally drink about a 1 gallon of just water a day, but sometimes I need something more than water when I'm working up a sweat. My 1 can a day is strictly a "normal" day. A few weeks ago when I was moving, I drank at least 2 pops and 6 sports drinks during the hardest and hottest days, as well as upping my water intake to nearly 2 gallons.
Quantity vs Cost:
You might not even realize how much you are eating in actual cost. You might get some real cheap food, but because it's not filling, you eat more of it and it costs you more than buying something more expensive. Chips and other corn or rice based snacks are a good example. I once bought a huge $3 bag of "cheesy puffs" and thought it would last for weeks. Because it was mostly air, I ate the whole bag and was still hungry.
Granola is more expensive, but it'll keep you full longer. A $3 box of granola bars will make you more full than a $4 bag of chips. Fruit cups and even pudding cups can be less cost, when you consider the food density and how long it takes to digest.
On the other side of that coin, you can probably get a 2 liter of pop for $1-2 and that has a lot more in it than the 20 oz. that costs the same $1-2. If you have a resealable sports bottle that can handle pressure, you can refill the bottle for less than grabbing a new one. That is, if you buy the bottles individually. A 6 pack of 20 oz bottles is $4-5, instead of $8-12 they would cost from a machine or vendor individually. And a 12 oz. can of pop can cost $1-2 individually, or $0.30-0.40 in a 24 pack case.
There's lots of things you can buy in bulk that will cost you less per unit than a smaller bag. Cheese is a good example. I use a lot of shredded cheese, so I buy a 5 lbs. bag, instead of the 1 lb bags. I know I'll go through it before it starts growing mold. It also freezes well, so if I see a good deal, I'll buy it an throw it in the freezer, if I don't need to open it right away.
Then there are concentrates, and not always in how you think. Dish soap is often sold in larger bottles as concentrates, which usually means there's less water in it. But then you can also think of salsa as a concentrate. If you like mild or medium salsa, get the same sized jar of hot and simply use less. If you already use the hot stuff, get a small bottle of habanero sauce and add a few drops to each use, and then reduce your salsa use, too. That small bottle will last much longer than the salsa and you'll likely reduce your salsa use by half.
Cereal lasts and stays fresh for a long time, so always get the family size. I used to buy 10 lbs. tubes of ground beef, too. The grocery store I got them at would reduce the price by $0.50 or more per lbs. doing it that way. Then I'd portion it out to 1/2 lb burgers and a few 1 lb chunks for tacos and other meals. I'd put most of it in the freezer and it'd last a couple of months.
Caveat: make sure that you are going to use the larger sized containers before it spoils. If you waste the food, you aren't saving money, so sometimes a smaller container makes better financial sense. I gave up milk, since even a pint will go bad before I finish it.
There's definitely a lot of ways to reduce your food spending, but the first thing you need to do is still determine what you actually spend on food vs non-food. You probably don't need to figure the cost of individual slices of bread, but the finer resolution you do your math, the better estimates you can make for how much you actually eat in a day.
Even though I'm no longer in the poverty category, I find it difficult to spend $20 a day in food, unless I'm eating out. And spending more than about $10 on a meal is something I've had to mentally overcome. (I have a hard time understanding how a fast food burger is $12.) Also, I still get cheap steak to grill, since if you prepare them right, a $5-6 steak can taste really good. And at 16-20 oz. it'll easily fill even me up, especially with an 8 oz. can of beans and 2-4 slices of toast. (Like I said, I eat a lot.)