Hi!
Those four are definitely great schools, but as you probably already know, quite hard to get into. I would consider expanding your list to add some less selective, but still great schools.
Bullying shouldn’t be much of a problem, and I don’t see why it would be worse in boarding schools vs public/day school.
Also, you said your kid is entering 7th next year, right? Are you applying for 9th in 8th grade? Groton has an 8th grade class which you can try to apply for next year, although, again, it’s extremely selective.
I would recommend some schools, although I would need to know more about your kid- What EC’s are important to him? Which subjects does he like most at school? Would he prefer larger or smaller schools?
sorry my post’s kinda a mess, although I hope you found that helpful 