You only get 8 private schools, so you want to pick wisely, assessing not just the programs and fit but your likelihood of admittance.
I don’t know the various programs you listed for your summers. Are they highly selective ones that colleges know? As you probably know, highly selective colleges were inundated with applications this year due to test optional, and that may be the case next cycle. You need more than good grades, rigor, and test scores for these schools. Is there something unique about you that stands out? Do you have a compelling story to tell through your application? Assessing this will help you choose your 8 private’s. Does your school have naviance? Is it a feeder to Yale, Stanford, etc.?
If you/your counselor assess you have a good shot at a tippy top school, you should check out Stanford. Obviously excellent for engineering plus.
We just went through this process with our S, also Jewish. He isn’t 100% sure of engineering, so wanted a program where he’d figure out quickly if it was for him and which offered maximum flexibility. We also wanted a Jewish population. We assessed that his likelihood of admission at Stanford (the only tippy top he liked) wasn’t good. And, given what he wanted, decided ED would give him the best possibility of getting in. You may want to consider this approach.
At any rate, I would suggest looking at Columbia and see if you like the smaller core for Fu students, and whether it gives you the flexibility you desire. I echo Northwestern, given the quarter system plus its whole brain engineering (where you delve into hands on projects and design immediately). Engineers can double major there (though be prepared to work!). Also look at Duke, which has a top biomedengineering program and a first year experience where you immediately get hands on experience. Duke also provides flexibility in taking classes in Trinity and has various certificate programs in different areas. Penn has some interesting engineering programs and you can take classes at any of their schools. JHU, could also be a great choice; it has a first year course that covers a variety of engineering disciplines. Wash U is also flexible, and has a variety of interdiscilinary majors, and it has a large Jewish population. There’s also Brown, with its open curriculum.
Case Western and U Rochester are both fabulous for their engineering and flexibility. These were liklies for our S based on where we live, but may be targets for you, again, look at your Naviance/school experience.