I missed this question.
I suggest researching the auto-merit schools. You know exactly what the cost will be before you apply. And you have even more options in this category as NMF.
Then move to the schools that offer merit tuition discounts to attract high stat students that may possibly bring you to your budget. Rhodes in Memphis. College of Charleston. Trinity (TX). Univ of Dayton.
Lastly go for a few competitive scholarships. Certainly try Vandy since you love it and Vandy loves high stats. SMU is another good one where you have a better chance. URichmond. Those are well-worth the effort. Keep an eye on the early deadlines and other requirements.