I did assume your family had limited income, based on your statement that you would need nearly all costs covered. If your family has income lower than $65K, I would encourage a QB app, even though most of the matched finalists have EFC 0/near 0. All of the QB schools are a reach, but it can be a powerful application program, even if you don’t match on Dec 1.
Drop Williams then, this is a good way to cull your list. I would strongly discourage you from doing a 3-2 program because of actual costs as well as opportunity cost.