I cannot tell you about gluten free products because if my kids have a problem with that I never learned about it.
However, saving at the grocery store is my forte`.
My wife and I spend about $25 per person per week for groceries and other consumeables like toilet paper, detergent, and pet food. So you should pay about $125 per week for your family. I also live in SoCal so our food prices should be about the same. The difference is our buying habits. The key to saving the extra $500 per month is your willingness to change.
No change in buying habits means no change in money spent. Its your choice.
First, lets dispell some myths.
#1. You save more money by doing all your shopping at one store so you don't spend your savings on gas. WRONG! Unless your car gets less than 1 MPG.
#2. Shopping at Sams or Costco will save you money. NOT SO, if you buy meat and fresh fruit and vegetables there. I find prices much cheaper at my local grocery stores when they have meat or vegetables on sale. And Sams is less expensive to belong to and the prices are cheaper at Sams than Costco.
#3 marked down meat, vegetables, and canned goods are not safe. WRONG! Those items are marked down because they are not pleasing to the eye in the display case. They are ok to eat. They are good to eat.
Get all the ads for the ALL the grocery store in your area. Read all the ads. Then go back and read the ads again, use the pen and circle the best prices on all of the things you want for the week or month. Then plot your routes to the various places you go each week. When you go by one of the grocery deals, stop in on you way home or on your way to somethng else. You save gas. Always stop by that stores bargin bin. (Where they place marked down canned goods or items they are discontinuing.) Buy what you use or what you would like to use.
When you find a really good deal, buy MORE that what you need over the next week. I like to use the example of spaghetti sauce and alfredo sauce. Ragu normally costs $3 when it isn't on sale. But when it goes on a really good sale, its $.99. So when its on a really good sale, I buy 12 of them. That will last me the two months until they have that really good sale again. You save $2 everytine you use a bottle of ragu. But don't be afraid to change brands. My local Stater Bros had Hunts spaghetti sauce for $.99 each. If you bought two cans, they would give you two packages of pasta (12 to 16 oz). So I bought Hunts instead of Ragu spaghetti sauce. You may say, "Well my kids won't eat Hunts". In my home, I always add spices and stuff to the pasta sauce so I never use what comes directly from the can or bottle. If you do that too, it won't make any difference what came in the can or bottle because you made it better. (I add mushrooms, diced celery leaves, hamburger, onions (brown and green), italian seasoning, pizza spices, and what ever suits me. I've even added enchilada sauce for a spicier sauce.)
If I find a bunch of the same thing in the mark down bin, I go to the store manager and tell him he has 30 of this in his marked down bin and that if he will sell it to me for a better price, I will buy all of it. Example: 30 cans of cream of chicken soup for $.25 per can. 23 cans of pork and beans for $.30 per can. I could go on, but you get the idea.
Fruits and vegetable I tend to buy at one of the "mexican" markets in my area. Rio Ranch Market had brown onions for 10 lbs/$.99. Sams had 5 lbs for $4.99 and Stater Bros had brown onions for $.99 lb. At Rio Ranch you could only buy one onion if you wanted and you would have paid about 5 cents. When onions get that cheap, I buy 5 to 7 lbs (50 cents to 70 cents) and then store them out of the frige under a counter and use them as I want. If I loose half of them to spoilage, and I seldom loose more than one, then I only paid 20 cents per pound. And I always buy the size that I will use at one meal so I don't put half an onion in the frige.
I have posted on several of these questions on mamapedia as have others. I hope you go back and read and learn.
ETA: The four most expensive stores in our area are Vons, Ralph's, Costco, and Sams in that order for meat and vegetables. Walmart price matches so I bought 10 bottles of Kraft BBQ sauce that was on sale at Food 4 Less at Walmart. I saved 8 miles of car travel and got the deal at Walmart.
Good luck to you and yours.