To the OP: DEFINITELY write an LOI to Umich if it is your first choice school.
Michigan likes students that SHOW INTEREST. If I were you (which I was, two years ago), I would send them an update letter with your fall grades and any new activities, once your fall semester ends. This of course assumes you are still a student, but if you aren't, keep reading anyway. In the update letter, mention your continued interest in the school, but hold off on committing yourself to the school until AFTER you have completed all of your interviews. That way, you can be sure that Umich is truly your first choice, and your letter will hold more weight. At that point, if Michigan is still your number one choice, send them a letter, tell them how impressed you were with the school (elaborate a bit here if you want), why it is your first choice, and that should you be accepted there, you would definitely attend. And if for some reason you are still on the waitlist in May, you could try supplementing your application again; always update on new activities and grades, and you could even have an additional letter of recommendation sent if it is from someone who really knows you and can give a fresh perspective on your character.
These are just my suggestions; I have to say they worked pretty well for me, as I'm now an M2 here at umich. And most importantly, don't get discouraged that you are on the waitlist; you interviewed very early in the game, so Umich already likes you. And what they told you on interview day is true: the waitlist DOES move a lot, so you are most definitely still in the game. Hang in there and hopefully everything will work out for you! PM me if you have any questions.