I agree with Iowa/Iowa State and Utah and would add Kansas/KSU and Nebraska as state flagships where high-stat (but not astronomical) OOS students can get scholarships that bring the cost down to at or near in-state rates. In particular, Kansas is in a great college town, and it’s maybe not as large as Illinois or Alabama, though I don’t know the precise numbers; I don’t know KSU very well but understand Manhattan is very nice as well. I did really like Iowa and both Iowa and Nebraska have urban campuses. You can easily see their financial aid info on their websites.
Here’s a merit aid table for Miami of Ohio, which isn’t too far outside your parameters in terms of size (somewhat larger). Also a nice (small) college town.
https://miamioh.edu/admission/merit-guarantee/
Note that Miami super-scores for admission AND aid, which might bump a student up on the table. Also, students improve their chances if they apply early. This is often true, so it is good to get those applications in early.
As noted in my post, I’m not sure about financial aid at SCU and Denver, but schools fall within parameters in pretty much every respect, and it sounds like they would at least potentially be accessible in terms of admissions. CWRU does give generous financial aid. I know a student from just a couple of years ago, obviously a strong student, but not a perfect applicant, and they were paying about $36k at CWRU and many, if not most, of their friends, had similar or larger scholarships. The vast majority of students get aid. Of course that changes year to year, and personal circumstances are tremendously important. But I do feel like the aid is generous at CWRU. Will it get everyone below $40k? No. But, in terms of merit aid, I’d like a non-NMF type student’s chances there about as well as anywhere that does not guarantee to meet full financial need.
I believe Holy Cross and Richmond claim to meet full demonstrated need, though obviously schools can differ with parents on the numbers, they might be “need aware” in admissions, etc., etc.
Anyway, the NPC is very helpful for schools that look interesting.