You certainly have a full schedule for your week, so I will suggest that your first stop should be
www.allearsnet.com, to check out the menus at the various parks. This will give you full descriptions of the menu items as well as prices so you can pick places that will fit with both your tastes and your budget. There are excellent counter service restaurants (CS) at all of the parks, with the notable exception of MGM. Counter Service there does not get very good reviews. Several CS places offer 1/2 chicken or 1/2 chicken & ribs ( Tusker House and Flame Tree Barbecue in Animal Kingdom, Cosmic Rays at Magic Kingdom, and Wolfgang Puck Express at Downtown Disney, for example). If one chicken would ordinarily feed your family, then this would be an option to order 2 of these, and maybe an extra order of potatoes/fries to share with the group, and break up the burgers/hot dogs/ chicken nuggets that you will see at a most CS.
Other CS like Peco's Bill and Columbia Harbour House (both at Magic Kingdom) have wraps and sandwiches that are very large, and could often be split with another person for a lighter lunch. The boys would probably enjoy the double burgers at Peco's Bills or Cosmic Rays, they both have toppings bars with a huge selection.
Epcot has all of the restaurants at World Showcase. Most of the countries have both a Table Service and Counter Service option.
Over at Universal, I can highly recommend Louie's, for pizza. It is a Counter Service restaurant, but lots of seating. We ordered a large pizza for our family of 4. The cost was about $16 total, and I think we had a couple of slices left over. You can also order pasta and pizza by the slice.
With only one day for each park, I think that it is imperative that you schedule which park you are going to BEFORE YOU LEAVE HOME. There is a lot to see and do, so knowing what park you will be attending, the opening and closing times of each, and what time the parades, shows, and fireworks take place is IMPERATIVE to you maximizing your enjoyment, and reducing your stress! If you have the "hopping" feature on your tickets, that might help as well.
On the Disboards Home Page, select "Theme Park" from the taskbar. From the new window that opens, select "Park Hours" from the Theme Park Information section. This will tell you which parks are open later during your visit, which might help in planning (particularily if your are hopping between parks).
Many people find that they are able to do rides and attractions with little wait time by utilizing the following strategy: Avoid the parks with the Early Magic Hours (once a week, each park will open an hour early for onsite guests only; it's a different park each day. Each park will also stay open 3 hours later, for onsite guests; again it's a different park each day). By avoiding the extra magic parks on their specific day, they are able to get more done at one of the other 3 parks because they are generally less crowded, at least at opening. To further complicate things, they recommend that you GO to the park that had extra magic evenings the night before (since many onsiters took advantage of that park the night before, and those who are up early will probably go to the park that is open early in the morning!).
Once you figure out your park schedule, check out the menus at allears, and see where you would like to eat. You may have more luck finding table service if you try booking for lunch. A late lunch (3:45) could be an early dinner! Buffets will be certainly less expensive at lunch, and will fill those growing boys! If you can't get reservations for lunch, at least you have the menus for the counter service so you can have an idea where you want to go. It will be crowded, so try eating at 11, or after 1:30 if you chose counter service. Don't forget to take advantage of your fastpasses. You can get the fastpass, and go have lunch or dinner while you are waiting for your fastpass return time. One of you can get the fastpasses for everybody while the others wait in line for another attraction (Most people don't mind if one person is joining their family in line!)
Also, pick up one of the Disney planning guides at your bookstore (the Unofficial guide, etc) will help you to plan which attractions are "must see". If each person in your group picks out ONE thing in each park that they most want to see, even if you only do those 5 things, your trip to that park will be a success!