All of the schools you’re talking about are a long shot for anyone. IMO fact that no one from your school has gone to Vandy is an advantage while the fact that BC has a history with your school (and others like it) might be a disadvantage because it’s hard to stick out from the pack when they see lots of other applicants just like you. And Vandy wants to bring in students from all over the country, so the fact that you’re applying from farther away is a positive.
The Peabody School also makes Vandy the best fit for what you’re interested in. I would definitely apply there ED II, knowing that it’s extremely competitive - as are all of these schools. Even for ED, their acceptance rate is just 18%, same as Duke. Give it a shot but be prepared to move on if it doesn’t work out.