Because my family size is different to yours, my reasons for choosing a resort will have no relevence to you and would probably show a resort that would not be suitable for you.
Some of the delux resorts will offer "day beds" that are a little like short twin bed. These would be fine for a 5 Y Old (they're adiquate for most kids up to age 7/8 unless they are VERY large for their age). For your group size I would consider the Contemporary. It probably has the most convenient room set up ( if you make sure you get a room with 2 queens and a day bed). Cost wise though it's going to be a close thing which is cheaper, one delux room or two rooms at a moderate and the 2 room option gives you an extra bathroom.
If the "woodsy" themeing is something that is attractive to your family you could consider the cabins at Fort Wilderness. These units would be perfect for your family size, give you the same feel as WL and similar access to MK. However these should not be considered a deluxe resort.
Your last option is a 2 bedroom unit at one of the DVC resorts ( VWL would be an obvious choice if available to you). The DVC resorts all offer spectacular units and are available through Disney. It is often possible to rent points from the owners for the DVC units, but this is a private deal between you and the owner, neither Disney or the owners of this site take any responsibilty if that deal were to go bad (I've never heard of that happening, but it could). Renting points from an owner could give you a 2 bedroom DVC unit for about what you'd pay for a deluxe room, but there are implied risks. Even if you were to rent from Disney ( or via Dreams) it's worth remembering that although the "headline" cost of the unit appears to be higher than a regular room the savings you can make by using the kitchen ( even if just for breakfast) could help soften the blow of that higher room rate. Depending on how you usually eat a couple of small changes in your vacation style ( bagels,cereal, OJ toast for breakfast and maybe a pizza and a movie night) could mean the actual total cost is suprisingly similar.
It sounds like you're going to have to make some compromises , so you need to decide what's the most important priority and what are you prepared to give up in order to give you the best vacation experience possible for your budget.
DD13, 
DS5 really want to stay at the Wilderness Lodge but I'm not willing to spring for two rooms. Now we can't decide on where to stay. Any input would help. 
Our kids are 18,15, and soon to be 13. We love the view from the tower rooms, love the fact we can walk to MK, and love being at a monorail resort 
