So I did a quick google search on merit aid and LACs in the south. Lots of old threads on CC came up. Here’s an example of what you’ll find: http://talk.qa.collegeconfidential.com/college-search-selection/1683456-comparing-lacs-with-generous-merit-aid-policies.html
“Rhodes, Sewanee (not East coast, but if you are considering Centre, not so different), W&L, University of Richmond, Elon all have good merit scholarships. W&L’s full-ride Johnson is awarded to nearly 10% of the class.”