Yes you can do it! It definitely sounds possible. We've pinched pennies many times just so we can go.
Eating is low on our priority list too - imo there is great food everywhere, so we don't go to WDW (or anywhere) to eat. So we cut corners there, similar to you, and also keep in mind you would have to eat at home, too.
And remember, the experience you share with your little guy will be PRICELESS. You may not remember what you ate, but you'll remember all the fun you have!
Be sure you let us know how it was when you get back!!!