I see the dilehma - with such a low eve to begin with... One option would be a Pergola. It would be open to the sky between joists, but then you could grow some vines up it with will provide shade in the summer. Clematis maybe? Otherwise, you don't have much headroom for slope and you'd collect a lot of snow load with a shallow sloped roof in Minnesota. You could have a frame strong enough, but it might look "heavy" compared to the house. Just some thoughts...
