By far, the best alternative , In my opinion, would be a grand villa using one of the DVC members to rent points. They are amazing with full kitchens, great dining rooms, huge living room and sleeping accomodations for 12 plus whoever you want in cribs or sleeping bags (Disney only provides bedding and towels for 12 plus those in cribs only.
If you need to you could add studios , one bedrooms or two bedrooms to accomodat everyone. These units are somewhat difficult to get because there is a limited number of them
We have helped families in the past by allowing them to rent points and loook forward to continue to do this for the next couple of years. Tahe families that we have helped havehave been really really happy with the accomodations.
It probably is the most cost effective option also, especially with this many people.