Ralph Brennan's Jazz Kitchen Express in Downtown Disney always struck me as fairly good prices for on-site. Another site shows conflicting info, but it looks like it's between $6.59-$6.99 for a burger and fries, or $9.99 for a platter with chicken and shrimp and fries. I reckon some sort of splitting could be arranged to keep you under $20.
http://www.wdwinfo.com/disneyland/dining/menus-detail.cfm?restaurant.id=534
Plaza Inn and Rancho del Zocalo often come up as "splittable" options, even in this thread!
If you go for the soup in a breadbowl, you can get the soup in a bowl with the breadbowl on the side, and then save part of your breadbowl for later. It might make splitting easier as well. Or even eat some of the bread with skewers at Bengal Barbecue (I've done that!).
The Harbor Galley in New Orleans Square reportedly sells large baked potatoes; you could maybe split 2 of them for something like $15 and then share a popcorn or another snack.
Though I'm not sure what you mean by $20 per meal...if you are thinking breakfast, lunch, and dinner, I'd definitely bring some breakfast fixings (even just instant oatmeal) and eat breakfast in the room, then put the savings toward lunch and dinner (or snacks, but I have a bit of a sweet tooth
). And/or, you may be able to have a large, late lunch and then a light dinner...that works well for me in hot weather.
El Pollo Loco is off-site and not walkable, unfortunately.