I would only EA not ED Since the price is a driving factor I would start looking at schools like Washington and Lee and their Johnson scholarship(full ride)
I hate to discourage but I think MIT might not be the best chance for your EA. If Harvard is #2 maybe give that a try. They do not use home equity in their aid calculations. You need to find a school with stacking aid. Most that stack seem to be places you would have a good package at. Bowdoin is a great school but not very well known for giving a lot of aid. My kid got a top merit scholarship and it was only $15,000 a year.