I would add Deerfield to your list.
Did you look at St Paul’s?
If you like animals, you should look at Millbrook - they have their own zoo and it is really fabulous. Students have the opportunity to take care of animals and think its an integrated program with Biology, as well as community service.
If you like sailing, marine biology, the ocean….check out Tabor Academy and St George’s (Newport).
Other schools that are not in the NE, but you should check out include: Mercersburg, Blair, St Andrews (Delaware), Episcopal, etc
For all boys: Check out Salisbury
For all girls: Check out Emma Willard, Miss Porter’s, Westover, Madeira (Washington DC)