I agree with planting chufas. They will absolutely demolish your field. HOWEVER, you plant chufas in the summer and they grow up until the first frost. As the plant goes dormant, the sugar level rises and the turkeys come calling!! They scratch, dig, paw, and chew until they wipe out the whole field. By the time spring comes around you don't have much left over to lure the birds unless you plant a BUNCH. I'm not saying don't plant it, I'm just letting you know what's coming.
Another suggestion is to plant some white clover. My personal preference is durano clover. The durano seems to have more stems and more mass than other white clovers. If you take care of it with fertilizer and mowing the tops of the clover, it will do well and turkeys love it.