You could also build narrow, long cages/runs to fit between your rows. Let the girls take turns in there and move it a row over every day. It doesn't need to be very tall. Think PVC pipe.
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I have always thought about a fenced in garden spot, attached to the coop or run, so that the chickens could be fenced OUT in the spring and harvest time, but given access after harvest and through the winter. The chickens would fertilize and till the soil and it would be easy to dump bedding there in the fall so it could age before spring. Just a thought...