Planning to plant new lawn
Oakland County Michigan
Congratulations! You have picked the best time of the year in Michigan to seed a new lawn.
FIRST: you need to do a soil test to learn about your soil type, it's fertility, organic content and more. Go here to get your test: https://www.canr.msu.edu/uploads/files/Soil_Test9-12RS.pdf
While you are waiting for the results, you could till the soil (2-3 in. deep) to loosen it and to be ready to add organic material if your soil test indicates a need. I would rather add organic material (compost, rotted leaves, rotted manure, etc.-think bulk, not bagged) to your soil than a layer of soil on top (which could also smother tree roots). Be careful about tilling too deep as you are under trees and will damage their roots. Your seed choice sounds good, but you might want to check with a turf expert at your local nursery for their opinion as they might suggest a better seed mix (mostly turf-type tall fescue and fine fescues for shade). I will also suggest that in the deepest shade areas (1st photo) you might want to consider a shade loving ground cover as all turf varieties like some sunlight to grow densely. More info here: https://www.canr.msu.edu/news/shady_lawn_alternatives
Articles that will help you in this process:
Good luck! By mid-late October you should have a nice lawn established.