I too wondered why Missouri S&T isn’t on your list. Excellent engineering school - stronger STEM than JMU.
Since you’re in a Midwestern Exchange state, you may want to look at some of the schools where you’d get the reciprocity rate. These include some flagship U’s like U of Kansas and UNL, and branch campuses like UW-Milwaukee. Institutions | Midwest Student Exchange Program
Already suggested up-thread is Iowa State, which should be both attainable and in budget, with excellent engineering.
U of Utah is another flagship option, as they have a path to residency for OOS students; you’d be well within your four-year budget, though the cost would be front-loaded because you’d be paying OOS the first year. Another school with great music opportunities in addition to strong STEM.
There’s also U of Maine, which offers a Flagship Match rate.
Some of your schools look neither attainable nor affordable (i.e. UT-Austin), but there are excellent substitutes that could work well if you prefer to go out of state. Maybe you could tell us more about why you like the schools you chose; I’m not really seeing clear commonalities that make clear to me what kind of environment you’re looking for.