You have strong mitigating circumstances and an excellent SAT. If I was going to ED anywhere with a BME focus, I would burn that ED on JHU rather than Columbia. Columbia is very expensive even if you get a lot of aid because you will be living in Manhattan. I am not saying you will get in at JHU but IMO ED comes with giving up the optionality of pursuing other schools, and therefore needs to be spent on the best possible school for you interest area/finances. Unless the Columbia COA will be far less than the JHU COA, I would reconsider.
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