If your D is only a sophomore, she has time to study for the PSAT with the goal of making National Merit Finalist. Lots of full tuition/full rides open up with this feather in her cap. Check out your historical state cut-offs and maybe have her take a couple practice exams to see if this could be a game plan.
Good luck & aloha!
OP here. Thank you so much for your advice! she is taking her first psat next week, so that will give us an indication of where the road might take us. I had an interesting e change with a college counselor yesterday about this topic. His suggestion was to be especially mindful of making sure the “fit” is correct for specific schools. he said that many of his students were surprised at the merit aid they had received when they focused on match schools vs reach, and strong demonstration of fit in applications. Really good information by all…thank you!!!
Here’s a few more to consider (not on the coasts, but might be worth a look):
University of Tennessee - Knoxville (Knoxville, TN) – good science and engineering programs: http://onestop.utk.edu/volunteer-scholarship/
University of Mississippi “Ole Miss” (Oxford, MS): http://olemiss.edu/info/admissions/admissions-finaid/#
University of Alabama- Huntsville (Huntsville, AL): http://www.uah.edu/admissions/undergraduate/financial-aid/scholarships
Truman State University (Kirksville, MO) – a public liberal arts and sciences college, although in a rural area: http://www.truman.edu/admission-cost/cost-aid/scholarships/automatic-scholarships/
Trinity University (San Antonio, TX) – less than 3,000 students, but might be worth a look: https://new.trinity.edu/sites/default/files/file_attachments/2016-17-scholarship-grid-august-2015-other-scholarships.pdf
I can confirm that “What you see if what you get” with regards to Trinity U’s scholarships. Plus, you have the chance to compete for a dozen or so full-ride scholarships too.
Good luck.
Wow, I had no idea that Trinity was so transparent with their merit formulas! That’s very handy info @ColdinMinny! We just visited Trinity weekend before last and were very favorably impressed. Their CS department looks truly outstanding for a LAC (we’ve been to about a dozen schools now and I think Trinity’s CS ranks right at the top with Carleton), and the other aspects of the school seemed quite appealing as well. Except the heat. Temps over 90 in late September are just wrong. Still, I think my son could get over that 
@ post #22: I should mention that the merit awards stated on the link to Trinity University appear to be competitive, and not automatic as the ones for UTK, Ole Miss, UAH, and Truman State appear to be. However, @ColdinMinny may be able to clarify that point about the Trinity scholarships on the link that I provided.
If you have X test score and Y GPA, that is the scholarship offer you will receive. As straight forward as it gets.
Plus, you then have a chance to compete for a set of Full ride scholarships, they call the Tower Scholarships, and these are indeed competitive. But you still always get the identified scholarship on their table.
I hope that makes sense.
^ Well, I wasn’t sure whether placement on the grid resulted in an automatic award. The website states that students falling within the listed parameters are “automatically considered” for the awards, not that the scholarships are “automatically awarded.” But I may be over-analyzing the language.
Another grid for another (non-coastal) school, the University of Alabama - Birmingham: http://www.uab.edu/students/paying-for-uab/scholarships/item/570-act-gpa-based-scholarships
RPI gives merit aid based solely on test scores. My son did not win a Rensselaer Medal but got the same amount of money (15K per year) as he would have if he did win it.
RPI has test scores as an input to their NPC, though the amount of merit aid was a bit less than predicted. It still was without applying for any scholarship.
If your child will not get any need-based aid, realize that she may still be able to get loans through the school. A certain amount of loans are up to the school, and my son even has a Perkins loan though we are definitely not considered “extraordinary need” like the Perkins description says.
I don’t think 40K of loans over four years for any kid, barring a very fluffy major, is unrealistic.
40K of loans would make me nervous, but I tend to approach money very conservatively, I guess. Possibly that’s because our area is so economically depressed; depending an a particular income around here is chancy. But on the bright side, we have purchased two homes in the last 20 years (needed updating but solid) and both of them were less than 40K 
.