Congrats on your hard work and success!
A student can get need-based aid or merit aid. You are focusing on merit aid. You might consider Miami of Ohio. Here’s a simple chart that shows the range of aid you might receive there.
http://miamioh.edu/admission/merit-grid/
I think this chart suggests that you might want to reconsider the decision not to retake the SAT, or to take the ACT. You can prepare pretty well for it with a limited amount of study in guides that are readily available. It doesn’t have to interfere with your AP classes. You note, “Some obstacles in my college search have been finding schools which will offer merit with my somewhat low SAT score.” This is something you can control. Why not give it one more shot?
Public universities offer little merit aid for OOS students. The University of Alabama has become well-known as an exception but requires high stats (which also argues for retaking the SAT). I’ve seen on CC that Alabama-Huntsville also offers merit aid, though I can’t vouch for that. Huntsville is home to NASA facilities and is a nice town. But in general, you’d be looking at private schools, like Denison, Kalamazoo, College of Wooster, etc., which often give significant merit aid but can still be pretty expensive.
You might also look at need-based aid. From what you say, you might not be in line for this, and/or may not receive enough aid to cover what your family is not paying. However, you can google schools that meet full financial need. These include most of the wealthiest, most competitive schools (Williams, Amherst, Harvard, Yale, Penn) but also some that are more accessible: Beloit, Clark University (MA), Berea, Holy Cross, Denison, Earlham, Franklin and Marshall, Gettysburg, Grinnell, etc. Good luck!