While they normally wouldn't go broody, I think your group will next spribg/summer because of how wildlike they are becoming. They are able to form nests and aren't losing their egg every day like most chickens do.
One of my flocks is somewhat similar, but probably closer to your barn flock. It's a group of around a dozen pheonixes and a Cemani pair that intermingle (~10 females and 2 males). They're fed once a day at night and sleep in the barn, but the barn is open structured and they are never locked up...