You are very cautious, which is good, but do not be self-restricting either. Apply to more inland good engineering schools.
Among Ivies: apply to Dartmouth (they receive less engineering applications since their eng. diploma requires 5 years, even if it can be done in 4 while sacrificing a summer)
Apply to U Illinois at Urbana-Champaign : top school a bit out of the common path location like Purdue.
Another good engineering school in the middle of nowhere is Texas A&M. Don’t think of U Texas at Austin as an out of state.
Also, a general advice. Most engineering kids apply to CS, while most engineering schools look for more interdisciplinary candidates with good CS skills, but able to handle Math, Chemistry and Physics. After you enter they will test what you are really good at anyway. So, my advice would be to expand your field in your application. If you have good grades in math and chem, apply to Materials Engineering. This is an emerging field, where your background in math allows you to look for chemical patterns, and CS can help you implement it. GeorgiaTech is building their name is Materials Engineering and if you sign up for an open house you will be blown away by the amount of CS modeling used. For something else than CS you can apply to GeorgiaTech too.