Thinking out of the box, while it is a reach financially, perhaps look at Wash & Lee. It is next door to VMI (there is an entrance and street connecting the two campuses) and allows cross registration and has some shared activities. With your D’s interest in military academies that may be appealing.
W&L is generous with need-based aid and also offers the Johnson Scholarship (merit based full ride) to 10% of the incoming class plus several full tuition merit scholarships based on region and other criteria (e.g. Jewish students).