I think you really need to have scores first. There is a big difference between some of those schools mentioned above. Some are much easier than others in terms of acceptance. The schools are likely to know your school. Have other students been accepted in recent years? That will tell you something.
While I don’t agree that any school is a grind unless a child is wired that way, I do agree that going to a school where things are going to come very easily to many kids and having to work 3x as hard isn’t a good fit. Much like sending a person who isn’t good in math to become an Engineer. There are many kids at many boarding schools who are drowning. They have been tutored and groomed since birth and here they meet kids for whom it comes easily and there is not enough time in the day. Can make for a stressful environment for some.
The schools you mentioned normally have kids with super high grades, many with amazing EC’s even in 8th grade and also high test scores. I think the test scores are the least important factor. But as a parent, I would not let my kids apply to a school to which they are likely not in the same mean as others.
Check out the schools mentioned. Some of them are good suggestions. Also, figure out which schools appeal to you AFTER a visit.