You can't take it with you. Spend away.

Lots of variables I'm sure.

The added costs I'm sure will keep adding up.

I would worry about cross ventilation issues (lack of achievement) with some of these designs.

If your looking for a flat roof I would think Spray Foam insulation would be a necessary addition to the mix.

Cost + + + +

A flat roof in Michigan is a gamble. Chances are it's going to leak sooner or later. There are precautions that can be taken to prolong it, but your best bet is to come up with a design that has some slope to the roof yet somehow resembles a flat roof.

Fall OUT of love! Even if the roofer guarantees it and comes back to "fix" it every time it leaks.....that doesn't make up for the wet furniture, rugs etc. I speak from experience!!!

I have worked on flat roofs in commercial and residential since the early 80's and the only product I will reccomend is http://duro-last.com/
I have never had an issue with it and it carries the best guarantee I have seen.
BTW, I also am a happy customer since this is the product I choose for my office because I didn't want any issues down the road and the light color i choose has reduced the heat buildup in the attic space.
I have no connection to the company but do love their products.

I had a durolast roof installed last year and have had no issues

how many feet of snow did you get this winter?

You can have a sloped roof that looks flat - Mark B is local to you / absolutely right. However, you will pay more in your structure to carry the snow load if you are not coastal MI - the build ups there are just not as big. You can hide a shed roof with the right proscenium at least on three sides . . so find a local residential architect who specializes in the genre you love .. . or go for a different kind of contemporary.