With time short for fall 2019 and tough odds to be accepted senior year, you could also consider a post-grad year between high school and college. Many boarding schools have a large PG class as a launch into college and also academic prep.
Much of what you are looking for/to avoid will be pretty hard to find as you are essentially describing many schools. However, you can also Google alternative boarding schools which offer non-traditional approaches such as a focus on the outdoors or specific EC passions.