Hi- slow response from me, the OP! 
I’ve been overseas for work and forgot to log in for the last week or so. I really do appreciate the advice and kind words of everyone. To answer some questions that have come up in the comments- he is considering the local university (NC State) as it has a decent engineering program. I think his odds of getting in are good. He has also looked at programs like Georgia Tech, Carnegie Mellon, Case Western, Franklin Olin. We’ve talked about long shots like MIT, but he won’t qualify for need-based aid and I’m not sure we would want to pay that kind of college cost, even if he was accepted.
He isn’t interested in a service academy, but will be trying for NROTC. He is quite fit, but I don’t know that I would say he is extremely athletic.
I really like @bopper (s) comment about writing out the family responsibility to make it clear what it entails, similar to a resume description, and @ChoatieMom (s) reminder that Eagle Scout is more than a single EC.
Thanks again to everyone for the ideas for different schools and approaches.