Regarding the movie topic, I also bring food into the movies because there isn't a single thing on their menu that falls into our diets. All of the artificial flavors, colors, etc. I want my kids to have as similar of a movie-going experience as their friends. We do purchased bottled water there, though. If the food options improve, then I'd be happy to make my purchase there.
Anyways, regarding Disney, I'd stalk Groupon, Living Social, and other deal websites a few months before the trip to see if there are any deals for nearby restaurants! Also, if you look at what restaurants are in the area, so many restaurants have clubs that you can sign up for. The last time that we went to a coastal town near us, I found a new pizza plate that had just opened, signed up for their email list, and got a coupon for a free large pizza with $20 purchase. We ate dinner there and then had pizza to warm up in our hotel room for the next two days! You have to sign up for a lot of those within a few weeks of going or else their coupons will expire though. What about Ibotta? Do you use that grocery app? You can use their digital coupons and then whatever money you have saved you can transfer to a vacation fund.
Our budget for our family of 4 for our 2016, 13 day trip (6 of those days being Disney World) is $4500 with $650 of that going towards meals. We have a few can't be missed spots that we'd like to eat at and we are going to splurge for one character meal, but I know that we'll physically just feel so much better by bringing a lot of our food into the park and enjoy using that money elsewhere. You can make "brown baggin' it" super interesting...cold pasta salads (Asian, Mexican, Southwestern), quinoa salad, various wraps, falafel hummus veg pitas, various types of pb&J. You can bring in cooked hog dogs in a thermos w/ some buns and then you can buy some french fries from CS restaurant and use some condiments there so it's a full meal. Make chili pie by getting some chili from Columbia Harbour House in MK and put it over fritos with shredded cheese that you can pack in - I think that two bowls of chili would easily stretch between 4 people w/ the fritos and cheese additions. If you make spaghetti and meatballs one night, save some meatballs for lunch the next day. Pop them in a thermos and pack some hearty sandwich rolls and cheese to make meatball sandwiches. Pigs in a blanket are fine eaten at room temp and I am happy eating those at any meal of the day. Fresh fruit, for snacks, is available everywhere but it's so expensive. Even fresh fruit packed in can save a lot of money and is very filling and satisfying on a hot day. I love a previous suggestion of bringing cheese and fruit and buying a baguette at Epcot! That sounds lovely. I'm planning on freezing some homemade lemonade and bringing it for some yummy (and healthier/cheap) slushies during the day. We usually drink plain water, but that can get old when you see everybody else with fun drinks!
Best of luck to you. I think you are doing such a fun and wonderful thing. Y'all are going to have a blast!