Up until the CBR opened in 1988 if you wanted to stay on property you had no choice but a deluxe or the campground. Things have come along way.
To keep prices down they started with moderates. They had one, CBR, , until PO-FQ opened in 1990. To help accomodate those with 5 people in their parties, they included a trundle bed in the Alligator Bayou section of PO-R.
The size of a room helps to determine how many may stay in a room--- AKL and WL rooms are the same size of CBR and they only sleep 4, but they cost more than the moderates. The larger the room, the larger the price. I know that it may not seem fair.
Have you looked into some of the Good Neighbor resorts on Hotel Plaza Blvd? You might want to look into the Best Western or Doubleday Suites, which could easily accomodate your family, save on food costs because you will have access to cooking, and still be the closest thing to on property as you can get to sleep 5 without paying a lot. They are also right across the street from a grocery store, TGIFridays, McDonalds, Perkins, and Taco Bell. You won't be able to participate in EMH and the transporation is nowhere near as good as Disney's, but if that isn't an important factor and you have a car with you, you should be OK!
Still, if you look for deals on Disney property, you can many times get two value rooms for the same price, if not less than the moderates will cost you.