I would think your high GPA in a demanding major will give you more of a chance at both places. Not too many engineers want to go to law school, so you might be that something different.
What about St. John's in New York? Catholic or American in DC? If you want to go to Chicago, maybe look at Illinois Tech (Kent) and Suffolk in Boston. There are other schools in each city that your numbers seem to shoe you in, and might make you a scholarship candidate--like John Marshall and De Paul in Chicago and New England School of Law in Boston.
Still, I would think your strong grades in a hard, unusual major compensate for your relatively low LSAT. (I say relative cause im tryin' to get in on a 154 and 3.15 in Poli Sci) And if your still in school--hit the pre law advisor at Villanova or some other school in philly if Villy aint got one. For what a fellow applicant's evaluation is worth, that 3.6 in Eng has to look like something special to law admit committees.