Michigan voting

I can't vote in Michigan. On September 13th, Patrick and I went to the Secretary of State Office (kind of like a DMV) to register to vote. After waiting in line for 30 minutes we are seen by a woman who, I think, wants to deal with us as much as she wants an enema. We hand her our NEW MEXICO driver licenses and explain why we are there. She takes the licenses asks what our Ann Arbor addresses are (and continuously tells me that I don't have a "real" address because it is a residence hall), hands them back to us and says we should receive our voter registration cards in the mail within three weeks.
Three weeks pass. Neither Patrick or I receive our voter registration cards.
I go to the Secretary of State website to find out where I am supposed to go to vote and (wonder of wonders) neither Patrick or I are registered voters in the state of Michigan. We are nowhere in their data base. I check the web site more thoroughly to find that my address on my driver license, by state law, has to match the address on my voter registration card. Keep in mind that the reasons that I didn't get a Michigan license were because: 1) my NM license is good for another 4 years, and 2) I can't establish in state residency in Michigan because I don't live in a "permanent" residence - which means that I cannot get in state tuition.
So, I try to call the office and of course, can't find a number that connects to anyone. So I email their "help line", explaining my situation. In the mean time I figure I HAVE to vote somewhere and I am still a registered voter in NM, so I send in for an absentee ballot for NM (which, as we all know, only has 5 electoral college votes as opposed to Michigan's 17). I get a response from the Secretary of State's office today telling me that it was a "clerical error" and I would have to come into their office to fix it. The same was true for Patrick.
I suppose that I could just go in and "fix" whatever clerical error they made and set up to vote here in Michigan. But, I am going to just file my absentee ballot with NM. It may be only 5 votes compared with Michigan's 17, but at least I will have voted.