U of Louisville is an obvious safety here. They have a great BME program (along with the Kentucky Spinal Cord institute) and a med school. I’ve heard wonderful things about the honors program, and that would give you a smaller cohort. Their engineering school has ~2000 undergrad enrollment, while WashU has ~1500.
Check out Mizzou as well. You’d get automerit, plus a little more for living in a border state. Their engineering is bigger at ~2700 students.
Dayton gives good merit and guarantees costs for 4 years. Their engineering enrollment is ~1700. All these schools offer honors to give an even smaller feeling.