Annual forage crop for headlands of row crop

I am looking into seeding the headlands of my sugar beet field into an anual forage due to the expensive costs of raising the beets. I would have 120 feet on each end. I need something that will keep growing in the fall to suck moisture out of the ground and hold the beet trucks up when harvest comes. We have seeded headlands to wheat put in a wet fall that turns to mush. Quality salable dry hay is what I'm after. Considering teff grass just don't know how long it will grow into the fall. My back up plan it to plant wheat then get a cover crop growing after wheats off. Thoughts of idea?

Annual forage crop for headlands of row crop