The colleges I listed do not require any reciprocal agreement.
Washington and Lee is a great choice. The Johnson Scholarship is awarded to a significant %age of freshman, and the school guarantees to meet full need…if you have need.
I’ll let @DramaMama2021 and @cinnamon1212 chime in.
Once your kids have first semester junior year grades and an SAT or ACT score, it will be easier to guestimate their chances for scholarships and acceptances. And yes…some merit scholarships require test scores.