I did the summer program at Lawrenceville, and I know a ton of people that go there. It is just as high stress at Andover and Exeter. There are Saturday classes that you have to attend. My TA told me everyone would be up at 12 doing homework.
I would take a look at NMH. It checks all the boxes. It’s very relaxed, but the academics are very good.
This thread is very helpful and would highly recommend checking it out.