When I had just seen your title and had not yet seen your list, Rochester and Villanova, along with Syracuse, were three that immediately came to mind. I would continue to view those as promising.
People obviously think of GWU first for things like international relations, but I have repeatedly heard good things about some other programs, including SEAS. It isn’t a huge program, but not tiny either. Their Science and Engineering Hall is relatively new, and appears pretty impressive:
And the bottom line is it is ABET accredited, including for Mechanical.
It also has an excellent location in a very fun city for students (not least because so much you can do is free). I can’t speak from personal experience to the vibe among SEAS students, but I would think it is a decent bet to be maybe at least a notch more chill than at some other notable options.