Costs are as hard to predict as admissions are because you’ll qualify for scholarships at a lot of schools, but in most cases you won’t know in advance.
As @tsbna44 has already said, the University of Tulsa offers free tuition and housing to National Merit Semifinalists.
At U of Alabama, you would at a minimum qualify for a presidential scholarship worth $28,000 and be eligible for additional awards.
Washington & Lee is particularly intriguing because it is a top 20 liberal arts college (your stated goal) and they offer full scholarships to the top 10% of the freshman class plus others to compete for. AND they are the rare liberal arts college which has its own law school. AND for someone interested in public policy, they have some very interesting majors in addition to the traditional Poli-Sci major:
- Law, Justice, and Society
- Education Policy
- Poverty and Human Capability Studies
- Environmental Studies
UConn has a number of generous scholarships for high achieving students both in state and out of state, some of which you specifically have to apply for. Check their scholarship page which has particularly attractive opportunities for in state students.
The following schools on your list all have acceptance rates below 15% (using out of state acceptance rates for state schools):
Georgetown
Ivies
Northeastern
Barnard
Virginia
North Carolina
USC
UCs
This means that while you are competitive for all of them, they reject students with your profile all the time. As you’ve said, a crap shoot. Some years ago, the president of the University of Chicago famously said, “If we removed our entire freshman class and replaced it with the next group, you wouldn’t be able to tell the difference.”
It’s good that you list Maryland early action because admission is impossible during regular decision.
With your profile, your best chances for scholarship money will be at colleges where the acceptance rate is above 20%. Everyone has their favorites among these schools. For pre-law, mine would include Union College (NY), University of Rochester (NY), Dickinson College (. PA), University of Richmond (VA), Denison University (OH), and Macalester College (MN).
The other way to control costs is at state universities with favorable out of state prices. University of Maine and SUNY Albany will match the cost of your in state flagship. In my limited experience, SUNY Binghamton and UMass Amherst have been partial to out of state students in recent years and have reasonable out of state tuition or accessible scholarships.