Sewanee offers four full rides annually (including room and board), and it has one of the most beautiful campuses in the country. That’s in a class of around 500, so the odds for someone with your profile aren’t too bad.
If you become serious about Sewanee you should definitely visit campus, perhaps multiple times. You should write an incredible essay. And recognize that four scholarships are offered–it doesn’t necessarily mean that any or all of the applicants who receive them will actually commit to enroll. Two years ago 4500 prospective students applied for admission to Sewanee. If, say, the top 10% of these applicants are competitive for the 4 full ride offers, any one of those students has a roughly 1% chance of receiving a full ride.