I would recommend the following, purely based on personal opinion.
Angels Crossing is definitely worth your while and is surely one of the better "deals" around.
Eagle Eye is right here in my backyard. If you play after 3, the fee is only $65. I truly love this course, I have played probably 15-20 times and still get pumped when I know I'm playing.
Shepards Hollow is a great choice. I'm not sure how anyone can bash Art Hills on this one. I would definitely play this one over the Orchards. I liked the Orchards ( I played with a 103 degree fever and later found out I had pneumonia) but Shepards Hollow is fabulous.
Forest Dunes I think is another winner. I have known the head pro up there for quite some time. It is probably in my top 5 favorite in Michigan. Spectacular practice area, and phenomenal greens, the fastest purest greens I have had the pleasure of putting anywhere. I also think there are quite a few good holes, and some really great ones.
Arcadia Bluffs is a must see. I know cost is always an issue, thats why I have only been up there once in the last three years. However I think you can play for cheap after six o'clock and depending on when you will be there and how busy the course is at that time (probably not very busy at all) if you play quickly I think you should be able to play before dark. Its $100 after 4 and $50 after 6:30. Do yourself a favor and play here, It is really a marvel.
Greywalls is another must see. IMHO opinion it is all of Arcadia. Imagine playing golf in one of the Lord of the Rings movies, that is what you feel like. It is so hard to describe, even with pictures. DO NOT WASTE YOUR TIME AT TIMBERSTONE (BTW I haven't played it) , IF YOU ARE GOING TO DRIVE TO THE U.P. PLAY GREYWALLS. I have never looked forward to any 8 hour car ride, but I would drive to Florida in a heatbeat to play Greywalls.
I have never seen Black Lake, although I've been meaning to get up there. If you do play, let me know what you think. If you need any other advice I'd be happy to give you my opinions and or other suggestions. The intinierary you already have will be good, add Angels Crossings, Arcadia, and Greywalls and it will surely be one of the great golfing experiences of your life. P.S. if you have access to private courses Crystal Downs and The Kingsly Club are both awesome, Crystal Downs obviously is hands downs one of the premiere courses in the country. Let me know if you need a Fourth for Eagle Eye, its literally five minutes away. Also dining / partying / where to stay options in the area. Good Luck, D.P.N