Is your 12K EFC based on now having 2 kids in college?
If you now have a kid in grad school, with the exception of professional school, the grad student is independent and can probably borrow up to the full cost of attendance as a gradPlus loan. Is. Your grad student in a PhD program or a masters? Your grad student may have to pay his/her own way to free up monies for the younger student to attend college.
Unfortunately, BU does not meet 100% demonstrated need while Dartmouth does. Are your current kids in college sophomore, junior, seniors? Does either one of them have a prospective internship to help defray some of their costs?