Hopefully some more experienced posters will chime in about schools that are generous with full tuition merit. In our experience, the non-competitive merit got us to on average about $30-35k/year (which is why I included the $ for Furman, Rhodes and Case for your reference). So I think your best bet is to research the competitive merit mentioned (maybe add Tulane as they award a good many scholarships) and also the schools @vistajay mentioned that offer auto-merit based on stats. You can look that up on each website as they spell it out. I linked Univ of AL as an example.
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