You can stay with 5 at POR as mentioned - we have stayed with 6 including an infant. In our opinion a crowded room at Disney is much preferable to not going on a family vacation because it gets too expensive. The family suites at the value resorts do not come with the
free dining. 8 days and 7 nights with dining this year their was about 1700 (incl. tax). - That was for 5 (infant is free) , included meals and 1 day base tickets, and waterview room. The 1 day base ticket can be upgraded to whatever you need. I don't know how many days you need. It is virtually the same price for adjoining rooms at the value resorts if you prefer that. If you do not find the resorts with dining on the disney online reservation than call- repeatedly. We started with 2 rooms at POP and then finally got an opening at POR. The only reason we chose POR (we have stayed at both) is that the bus schedule and crowds are much better at POR (in our opinion) and the pools are much less crowded. It is an even split on which place is more fun....
Though the initial dollar amount is less for an offsite room - do not underestimate the cost of all the "extras". The rental car , the parking, the gas , all the meals and snacks,the long walk at the parking lots or waiting for a shuttle to get to the front gate, the fact they do not have the base ticket to start from (yes- you can find "discounts" on the base ticket - with 5 tickets you may save a total of $50 combined or less than the cost of a single base ticket) and the fact that IMO it is more stressful to drive around down there not really knowing where I am going than waiting for a bus ever was. It is for the most part much quicker to get on bus and go to resort than drive off premises to hotel. Also with a family going , there is the option some days or afternoons for 1 adult to go back to resort with some children while others continue to play (especially helpful if one child is not feeling great or gets too much sun) This is very difficult sharing a single rental car.
If you do decide to try to book on wdw property if they cant get the dates you need ask them to try to book for longer period (7 /8 /10 days) then after you make ressie call back and cancel the extra days. Sometimes there are rooms available somehow for a longer trip that do not show as available for a shorter trip.
Good luck and have fun !