It's certainly not to late to plant a plot. In fact, here in West-Central Illinois the ideal planting time for a Fall plot is between Aug. 1 to Sept 15. For a fast growing easily broadcasted planting then I'd look to a Oats/Wheat/Brassica planting. In fact, I would suggest Bio-Logic Green Patch Plus, it's cheap and super easy to grow.
Buck Forage Oats is also a super easy to plant choice and it grows extremely fast. You'll have a thick, great lookin' plot in only a couple weeks.