There's the option of seed germinating while you're still digging.
Steve Solomon has developed a homebrew hydroseeding method, where seeds are sprouted in trays, and just as they begin to germinate, they're gently mixed into some gruel, and applied using a plastic bag with the corner snipped off (essentially, a pastry bag).
The starch from this method will also add some degree of early erosion-resistance.
I can't rely on frost to kill much of anything in my climate.
Might I recommend amaranth as a seed-mat-former? I've noticed it's also quick to germinate. I've read good things about millet in that regard, too, but don't have much
experience with it.
"the qualities of these bacteria, like the heat of the sun, electricity, or the qualities of metals, are part of the storehouse of knowledge of all men. They are manifestations of the laws of nature, free to all men and reserved exclusively to none." SCOTUS, Funk Bros. Seed Co. v. Kale Inoculant Co.