We have stayed offsite at Bahama Bay Resort, Wyndham Bonnet Resort, and Reunion Resort. Each of these are very nice and would be great for a large family. All are large condos or town homes that offer 2-3 bedrooms, 2 bathrooms, kitchen, living room, and a deck. Prices vary depending on time of year, how far in advance you book, and mostly on how diligently you look for deals - but in general they cost less than one room in a Disney moderate. Check VRBO, eBay, and some of the re-sellers mention in these threads.
You will need a rental car (unless you are driving your own, of course), but these can be found very cheap if you search long enough.
You can save a lot by eating a few meals off site, either in the condo or at non Disney restaurants. Easily enough savings to cover the rental car, perhaps a lot more.