I also think you are likely to find there are many different great careers open to people strong in Math besides engineering, such that you might not do that. But I see no harm in it being an option.
If it were me, I’d probably add a couple more colleges which are excellent for Math and engineering, which are Targets or Likelies for you, and where you might get merit. You may not need it but it can be nice to have the option. Minnesota and Stony Brook are both publics I would recommend. Rochester for a private. I know Minnesota is not on the coasts, but the Twin Cities make up a vibrant, diverse, globally-connected metropolis. Rochester is also a bit off the beaten path, but it is a great college for people with diverse STEM interests who want to explore options thanks to a flexible curriculum.
Finally, if you are interested in exploring smaller colleges, Harvey Mudd and Cooper Union might be worth a long look.