Welcome!
Fitting six can be tough! WDW standard hotel rooms fit a max of 4 in all Value resorts and all but one Moderate (Port Orleans-Riverside, and they only fit 5 in certain rooms with a trundle bed). The deluxe standard rooms can fit 5.
For six, you have several options. You can rent one of the villas, which while are mainly for the use of DVC members, can be rented out, but as you've found out, are very expensive. You can try to rent points from a DVC member that won't be using their points for this year, you can get more info on the DVC boards. This is a very economical, but I'm not sure if it's cheaper than two hotel rooms or not, since I've never done it or researched it.
You can rent a cabin at Ft. Wilderness Campground. They sleep 6, and have a full kitchen. I stayed in one once, and I loved it, though the transportation withing the campground to connect to the buses and boat to take you to the parks is a bit anoying. Also, I believe that the Wilderness Lodge offers deluxe rooms that can fit 6, but I don't know too much about that.
Your best bet to keep costs down is to get two standard rooms at either a Value or a Moderate resort, and request connecting. This will be the cheapest way to go, plus you get two bathrooms, two t.v.'s, and you can shut the connecting door if someone needs a nap while the others want to be up and about.