What is your plan for funding your last 2 years of college? It sounds like your family will not qualify for any financial aid? That means merit aid and loans? Or will you have significant savings built up? There are severe limits on loans that students can take out each year. Larger loan amounts would need to be taken out by parents (although if they trust you to do the repayments, this might work.)
If you plan to go on to grad school of some kind, you might want to consider lower cost colleges.
You still need to calculate your uwGPA. It is not difficult at all if you know your grades from each class. For UMich, are you considering CoE besides Ross pre-admission? Ross is always a reach due to the low admission rate. CoE is slightly easier but OOS admission rate is still at the teens. It is hard to chance without knowing your uwGPA as UMich consider GPA to be most important.
Harvey Mudd as about an 18-19% acceptance rate, but the applicant pool is highly selective and qualified in engineering and the sciences. Your SAT is close to the 75th percentile and your other scores and GPA are competitive. I think that if you put together a compelling story for engineering+business but with a strong liberal arts background that you would be competitive. I think the Claremont college environment would be a great fit for you.
Rice has about a 15% acceptance rate (about 20% for ED). Your SAT is above the 50% percentile. They offer an undergraduate business minor through the Jones School of Business, so you could potentially do engineering with a business minor and get a liberal arts background. Houston is the 4th largest city in the U.S., and Rice is near the Texas Medical Center and in a decent neighborhood; it’s not the “deep south”. The undergraduate class is small (a little over 900 students per year), and they have a residential college system.
Vanderbilt has about a 13% admit rate. Your SAT is close to the 75th percentile for admitted students. It’s in Nashville, which is certainly in the south, but which is also a lively city and a great contemporary music city, which might be a plus given your music interests. There are more students from Massachusetts who currently attend than from either Virginia or North Carolina. They have a solid school of engineering, but you would be at a major liberal arts university. The Blair School of Music could be a plus for you.
Swarthmore is known to be pretty rigorous, but it’s a terrific school. The admit rate is about 14%. Your SAT is around the 75th percentile for admitted students. I’ve heard they tend to value depth of interest, focus, and “fit” a lot, but don’t have detailed knowledge. I think their theme of engineering within the context of a liberal arts education would be right up your alley:
http://www.swarthmore.edu/engineering
Just a few options to consider.