agree with Dave. Ideally, it should be a biennial which dies this winter, so you have no re-seeding problem. I use forage chicory, but not really as a cover crop, mostly to underseed things and get extra greens. Also, it does not die in winter.
one of your best bets is sorghum scythed once. It will not make it to seed that way, and will die at first frost. It is a superb soil builder, with deep roots, and huge amounts of organic matter. It is really the #1 summer cover for everyone, along with cowpeas and sunnhemp (legumes both), which you may also want to consider. With everything in that bed 7 ft tall, you will have very few weeds. sunnhemp does not seed anywhere in the USA except Hawaii, being a truly tropical legume, so with that cover you are totally safe even if you do nothing.
Q