^^^^^ This. Its difficult to grow in clay. In lieu of layering some good top soil a nice layer of hay would do some good. It will hold things in place and as it decays it will supplement the soil.

Another alternative might be anti erosion matting. Put your seed down and cover it with the stuff.

I have done both with success.

Pic 1 Hay
Pic 2 Matting
Pic 3 Grass