We really thought the Ice Cream Social at Garden Grille was a great deal for us. Even though some think it is expensive for ice cream. The ice cream was special, the restaurant deserted -- we had characters to ourselves. Hilarious. Kids loved the revolving feature too. We just couldn't justify the bucks for all 6 of us (4 kids, ages 5 to 13y) to eat at a character MEAL. Now with 2 11-year olds it may be different for you, but I do recommend looking into it. Great memories there. Also surprised DH & kids with a "re-hitching" there.
Our frugality with food also meant we splurged on a Kitchen Sink at Beaches & Cream 1 day. Again great memories. So the kids had Disney Magix cereal or Instant Oatmeal with dried fruit & nuts, etc. (both a treat in our family), granola bars, PB, pepperoni stix, bagels, GORP, juice boxes, our own bottled water using Brita, etc., Microwave Popcorn in eve lots of the time (16 days). No one was complaining or felt bad about it! For only 4 days & with the Searches on these great boards (especially regarding the collapsible coolers, ice, & Microwave at All-Stars). I'm sure you will have a fantastic & still healthy time on-site around the clock.
We had each kid wearing a Waist-Pouch with 2 snacks in it. I had purchased a bunch of mini-candy packages (gummies, etc.) at after-Hallowe'en large clearances. So big treat for kids to get these daily. Also get the Disney gummy treats in box (Betty Crocker? Toy Story, Princesses) when on sale. Protein is the only thing you need to put some extra thought too. Tuna Salad pkts also easy. Plan it out & budget for some Park meals & treats balanced out (like croissants at Epcot's France, Pecos Bill's in Magic Kingdom, a turkey leg, a Mickey Bar, whatever!!) and you won't feel you had to pinch & starve the whole time. Much easier to go back to your room or the Microwave at All-Stars if need be for meal that day if you're on-site than to HIFS without a car.
I also really recommend going to the Campfire at Ft. Wilderness as you'll be an on-site guest. Can try to take your own ingredients for S'more's with you, but really I thought was reasonable enough to buy there. Sorry, can't remember $5? for pkg WITH the stick! Lovely evening ferry ride over (saw the Electric Light Parade), sing-along, making S'more's, outdoor Disney movie on big screen. Can't do this if you're at HIFS. Others have recommended the Trails End Buffet or Pizza as good family affordable place to go. Again, SEARCH on Boards.
Long post, sorry, but I loved HIFS & in this case would really go for ON-SITE with advance planning! It is SO do-able & magical.
Have fun!