Corn gluten meal might be an option. It won't allow seedlings to live. It's effective for about 5 weeks. Once the season is over and the garden is cleared, I spread it on the soil. By early spring there are only a few weeds.
Not sure if this will be cost effective for an area your size. I got a big bag from an Amway in horse country over in Jersey and it was pretty inexpensive.
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