Can’t say which colleges will help with your EFC.
Check net price calculator for private colleges that use CSS PROFILE to determine financial need.
Have you any options for free community college and transfer? See program at West Virginia University for example.
https://admissions.wvu.edu/academics/majors/medical-laboratory-science#kf-taa
https://admissions.wvu.edu/how-to-apply/transfer-students/transfer-articulation-agreements