You need to spray first, let it die, spread the seed, drive through it with a 4x4 to make the seed make contact with the ground, then mow it. The thatch from mowing provides mulch which will keep the moist with the morning dew, and keep it warm. This also starts the process of building organic matter. I think Buckwheat would be a good start now. Then winter rye in the late summer, or whatever