I will be going into my sophomore year at West Virginia University. I am a civil engineering and air force ROTC student on scholarship. When I was in high school I applied to USNA, and it was my first choice. I unfortunately didn't get in. I still decided that it was something that I wanted to pursue, so I applied during my freshman year at WVU. That time around, I got waitlisted - but eventually didn't get a spot. I'll be re-applying again this year, and hopefully the third time will be the charm. Considering what you have told us already, and reflecting on what I've been through and what has resulted, I have some advice/questions for you. Perhaps we can bounce ideas off of each other...
1) It seems like you like Michigan, so I would just stay there and do AROTC. The school has a lot to do with how well you perform academically. Sure, NROTC would probably be better for USNA, but overall not that much. Even though they can't give you a nom, you can still get a letter of rec from the cadre there - which is valuable. I was able to do that at WVU with AFROTC.
2) I would stick with political science - or just do something like "general studies". Engineering is a lot of work, and unless its something you really want to do - it will be a huge pain in the but. I am pretty sure you can still take calc and chemistry as a polysci major, because every university is going to have math and science requirements (regardless of major) and I am more than positive those two classes will cover those requirements.
3) I know my congressional district automatically nominates me just because I received a nom in the past. Literally all I had to do was e-mail the secretary, and it was done. IDK if your reps do it the same way, but I would suggest asking
4) Whatever you do, make sure it is what YOU want to do. Because if you don't get in the 2nd time, you'll be stuck with that plan. In my case, I got wait listed and then a month later found out I didn't get in. Despite that, I have a GREAT plan that is already going for me, and I really had nothing to lose. Don't put all your eggs in the academy basket, because you'll be devastated if you dont get in
Hope this helps man, if you have any questions contact me. I'll be starting my USNA app for the third time later this month probably. Good luck