We did it last summer I just went to Google maps and found the roads closest to the lake.Gas is not a problem there are plenty of stations along the way.Google maps will tell you the mileage from one place to another so you can plan how far you want to ride each day.Also don't forget about Door County in Wisconsin you could pass it or if you have time it is a nice ride to go up one side and down the other.
Sorry you didn't get exactly what you were looking for,... hope your still watching this thread.
I'll be at the Dells Spring Ride/In and will bring a Michigan map for you. We can go over it together and can mark out the route "I" would suggest and have taken myself.
I live about 10 miles south of Grand Rapids and have a spare 'guest' bedroom with a queen bed you and your brother are welcome to use. I'll have to qualify the availability though. We're having our 50th anniversary celebration for a few days starting June 14th. After that, I'll probably be going to the SMRI. So depends on how your 'early June' is.
We overnighted in Luddington and took the morning boat trip over and really enjoyed it, coffee and cribbage on the way over helped pass the time! Even though it's not cheap it's certainly better than being stuck in Chicago traffic.
The Lake Michigan tour is fun but IMO the circle tour around Lake Superior is far better but takes a bit more time but not much and well worth it.