Getting late...do you have 6 weeks before frost? Warm soil temps? our soil temp is 59--warmer than usual. A neighbor put in seed on new lawn about 7 days ago and watered well. His new grass is up to about a half-inch tall in spots. (Scotts "Turfbuilder Sun and Shade".)
I suggest: power rake and rake up the residue. Lime as needed. Apply starter fert, plus seed, followed by dragging to work the seed into contact with the soil. Omit aeration unless soil needs it. Use the residue of dead grass to cover the seed like straw. Use double the usual amount of seed--just to be sure. That is cheaper than straw, and easier, too.
Be sure to use a top-quality seed that has around 50 percent perennial rye. Not enough time for bluegrass to establish much. You don't want cheap seed due to disease susceptibility (such as red thread, dollarspot, gray leaf spot and rust). Make sure the seed has endophytes for insect resistance.
Soil temperatures--perhaps slight cooler than my area.