My D had similar stats and is also premed so she was looking for merit to preserve her education savings for med school (we are full pay). She did not apply to colleges that do not offer merit. The colleges that came in under $40k with merit “tuition discounts” offered with decision.
Furman
Rhodes
Case Western
Our in-state unis (because of in state status it is free tuition, no merit offered)
She also applied for competitive merit. She considered all of these reaches as she would not attend without merit. If you decide to pursue competitive merit, keep in mind that some require your high school’s nomination and most have early deadlines for applying.
W&L - Johnson Scholarship (awarded)
Davidson - James B Duke (alternate) and Belk (was not a finalist)
Duke / UNC - Robertson (was not a finalist)
UVA - Jefferson (was not a finalist)
Vandy - Cornelius Vanderbilt (was not a finalist)
I agree with the suggestion of Miami Ohio. That’s a no brainer if you don’t mind the location. 
ETA: She was accepted to all of those except Duke, UNC (waitlist) and Vandy (waitlist).