It's a very good point that @gardenstategal makes about structure. My older DS (now a freshmen) has ADHD and after struggling for many years (undiagnosed and unmedicated) finally got things together in middle school, with a lot of teacher oversight and executive functioning tutoring. His heavy sports load also forced him to learn time management. We were hopeful that the structure of BS itself would go a long way toward helping him focus and stay on track with his work, and it has. He wasn't recommended for any formal Learning Center help, but between the pretty rigid schedule (including supervised study hall first term for freshmen) and teachers being very hands-on and readily available, he has done as well as he did when he was at home. Particularly in the fall when he played a varsity sport, he was extremely busy, but his time was also very compartmentalized, and it wasn't like he was deprived of study time due to sports, because everyone is doing some kind of activity. Being a bit less busy and structured over the winter, his grades have slipped a little. I think the kids really learn to appreciate the structure.
My younger DS does have diagnosed LDs and he would need more tutoring and academic support, but I think that the structure wherever he goes will be a very helpful piece for him as well.
We had visited LA a couple of years ago and have heard good things about it, but the one criticism I heard (from an acquaintance who is a SS consultant) was exactly what you said -- with roughly half day students, it does empty out on weekends, and there are not a lot of structured weekend activities for boarders. Of course, that's just one person's observation.
I agree. It was relatively easy for us to visit schools during 7th grade, and if you can do it, I definitely recommend it. Although the typical approach is to do a tour and interview at the same time, we scheduled some tours-only during 7th grade. Schools are pretty accommodating. The only thing to take into consideration is that spring break is long, typically 3 weeks in March, so students would not be on campus, and that revisit days are typically the last week of March and first week of April, so that would not be good times for an initial visit.
I will mention something else about the schools with a large day student population, and from your list, specifically AOF and Westminster, which are both in suburban (by CT standards) areas and draw heavily from the local neighborhoods. When you get up to a 20-25% day student level, I think the school atmosphere/culture seems to feel more like the local area and reflect its demographics. That may not be meaningful if you are from far away and aren't familiar with different towns, but it was a factor for us and my son. For applicants from outside the area, it is probably a matter of just determining what "feels right" (in addition to all other, more objective, factors), which is hard to do without visiting. If at all possible, I think visits (while school is in session) make a big difference. The brochures and web sites all look perfect, but it's so hard to really know without being there.