It would be a lot easier to be an engineering major and take additional math, physics and computer science courses as electives than to try to get the minimum required engineering courses for grad school purposes. Many courses are cross listed as well. Plus- a lot of the needed advanced (beyond the calculus sequence) math will be included in the engineering courses. So, instead of learning theory that is irrelevant to your major you get the needed math and physics principles. Different focus for pure sciences and engineering- you need to decide which one.
Just reread and noticed you’re from Michigan. Check on all three main Michigan schools for engineering- Michigan, Michigan State and Michigan Tech. Find out what grads do with their undergrad degree- eg do most stop at a BS and work or do enough go on to at least a masters. You want to have a peer group with similar aspirations for going beyond the BS. Look at what is offered in various majors. Figure out which campus you like best (not everyone wants the UP). Compare these programs to other states where you MIGHT get merit money.