I know many CC posters will disagree, but I believe OOS publics are the worst choices. Whatever the level of student, you pay much more for the same thing. Is OSU really any better than Birmingham or Stony Brook? And most flagships give admission advantages to instate applicants. So an OOS student will pay more while being near the top academically, while at LACs the opposite is true, as the best students are most likely to get merit. (Alabama and a few others are exceptions).
Tufts and other privates (and some publics) require the CSS profile, which does consider home ownership and equity. I’m not sure how the OP’s family’s unusual home financial situation will play out there.