That looks like a tough site for Kentucky Bluegrass. West facing, sloped surface, quite shady, competition for any moisture by mature trees, and I suspect sandy soil.

 There has been recent research to develop shade and drought tolerant lawns with success growing fine fescue varieties in lieu of Kentucky Bluegrass. I suggest you consider them. Here is a link to more detailed information on planting and maintaining fine fescue varieties: https://extension.umn.edu/lawns-and-landscapes/planting-and-maintaining-fine-fescue-lawn#management-characteristics-of-fine-fescues-3238010

A good place to start is with a soil test to determine soil make up and what fertilizer requirements might be. The twenty dollars or so that a test cost can save you a lot of re-dos in the future. Here is a link to soil testing information: https://extension.umn.edu/managing-soil-and-nutrients/soil-testing-lawns-and-gardens

Mid-August is an excellent time of year to seed lawn, or as you suggest dormant seed after the growing season. Link to dormant seeding information: https://extension.umn.edu/lawns-and-landscapes-minnesota/dormant-seeding

Paul -Master Gardener volunteer