Getting under 40K/year on merit alone, at private colleges and universities, will require big merit awards - even a half-tuition scholarship won’t get you to your threshold at most schools. The sticker price at OOS publics will be closer to your budget, but it will vary whether enough merit is available to close the gap. It may not be wise to rule out in-state publics out of hand.
Major-wise, I see where your thinking is going, in terms of econ offering more of an employable skill-set than poli sci. That doesn’t necessarily mean, though, that your daughter will want go the route of a deep dive on economic theory. There are some great options in the more applied, interdisciplinary majors, like Public Policy Analysis, Data Analytics, and the various flavors of “PPE/PPEL” (Philosophy, Politics, Economics, Law).
Even though you’re not liking the idea of OH publics, OSU is terrific in terms of these kind of majors, and thus a great place to compare pathways and think about what kind of program she would like best, even if that’s not where she’s going to end up.
https://glenn.osu.edu/academic-programs/undergraduate-degrees/bachelor-science-public-policy-analysis
https://artsandsciences.osu.edu/academics/majors/philosophy-politics-economics
Just outside of Columbus, Denison is also excellent for these kinds of majors
https://denison.edu/academics/politics-and-public-affairs
https://denison.edu/academics/data-analyticshttps://denison.edu/academics/data-analytics
https://denison.edu/academics/philosophy-politics-economics
They’re pretty generous with merit and the Lugar Program is a big plus Lugar Program | Denison University
As a general rule, anything that imparts a quantitative/computational skill-set will help with employability after undergrad. (GIS is another skill-set in this category that can be very useful, and geography-related majors that include GIS skills could be worth considering as well - here’s another OSU example: GIS and Spatial Analysis | Department of Geography )
For affordable schools in the WV-to-NY corridor, you’ll want to look at a combination of publics that give merit and/or have lower sticker prices, and LAC’s that discount heavily (like Juniata, Allegheny, and others in the CTCL genre College Profiles – Colleges That Change Lives )
It will be a stretch for Pitt to be affordable, but it could be a great choice if the money works. Temple has good potential, as already mentioned above. The SUNY system is a good place to look. TCNJ gives merit that might get to your price point. Geographically speaking, you’re targeting the highest-demand corridor where it’s hardest to get discounts, with the possible exception of WV. Widening the search in any direction (i.e. NH/Maine, NC/SC, and the Midwestern states) will turn up more bargains.