Well, now it is easier to see
in 2017, taking the yearly totals and dividing by 12 it looks like this, (I did not include dates nights as that amount isnt a large part of the spending at first glance):
eating out ( fast food, family eating out): $416/month
groceries : $576/month
So, to me, growing or processing your own isnt the first step. Almost half of food money spent is for eating out, buying drinks out.
There are many ideas for this. I can give you a few that worked for us, but, again, would need more details on lifestyle for your exact solutions. SO, you need to figure out times of day eating out, lunch ? Dinner ? Snack time ? Then, if bought drinks are very much of it, that is something to make note of.
So, I am just brainstorming here, since I do not know the details
For example, bought drinks solution might include : Making coffee at home and taking with you in a portable thermos, there are an awful lot of options on these I have seen my grown kids use, stainless steel, well insulated. They save alot of money making good coffee at home and taking it with them. Every adult and child could pack a cold drink bottle before getting in the car. You can decide wether this contains just water, as would be typical for my family. Or, it could be a water bottle with a water/fruit juice blend in it. If the kids are small and will not go thru so much during the day, you can have a larger bottle of your preferred mix, in a cooler even, and a few metal cups( see Lehmans catalog to buy) or plastic sippy cups for the littles to serve them theirs.
Another idea is to always have food with you in the car. Sandwiches, a sandwich is healthier than MacDonalds. Cheese, lunch meat or peanut butter, it does not need to be fancy. They keep well, otherwise my generation would all be dead as we took mayonaise and lunch meat at room temperature to school, but you can always just keep a cooler in the car. Fruit. Homebaked cookies, zuchini bread, bread maker bread with butter and jam.
If kids activities keep you out in the evening, you can switch things up by having a hot lunch and a sandwich dinner. Or, I used to use a solar oven or a crockpot to make sure there was food ready when we got home. You can also just microwave what you have cooked the previous night, so always be cooking a day ahead. I do know how hungry they are and how impossible it is to think of cooking when you just get home. However, it is much easier to think of cooking once you are well fed, so cooking or meal prep can happen in the evening after dinner for the next day.
I have brought a thermos of hot food for a younger sibling to make it thru the older ones practice or game. Many leftovers taste good cold too.
My youngest was out of the house alot in her teen homeschool years and would pack lunch, snacks and dinner, and she was an athlete and so this was ALOT of food. So, maybe one thermos of filling soup, bread and butter and a container of apple crisp for the hot meal; a thick sandwich or two and fruit for a cold meal; some yogurt, cookies, hummus and veggies, dried fruit etc... for snacking.
This will save ALOT of money if you do it often, it adds up. Not to mention it will be better nutrition for the kids and save alot of trash and other toxic gick from release into the world. Maybe it could be a family project where the kids help and the money saved goes to a special account for something the household wants or needs ?
While at first glance, it may look like work, once it gets going, it is very smooth and I think alot less work that keeping pigs or chickens and slaughtering and canning. The potential money saved is alot more, given your current budget, too
Since I was a "mean" mom, realy just a very tired mom with a big age gap between kids, I finally came up with a system where the older kids did an hour trade for all the time I spent driving them to activities and sitting around, and choices had to be made on how many activities each, like maybe one each per season, and yes I know that does add up ! We are at least 1/2 hour each direction from town, but the destination often further in. This means they would do extra help, beyond their chores, meal prep or clean up, laundry. Doesnt have to be all on a weeknight when they have homework, they can help do the weekly baking or ahead of time meal prep with you on the weekend ( chopping meat and veggies for the soup and put into a container, etc...)