I don't know about others experience but I've never had trouble with my hens laying anywhere except the nesting boxes. I keep them confined until they're laying reliably and then free range them. Although honestly except for the occasional "surprise roost egg" they've always taken the hint...
We have a heavily wooded area as well but our girls free range. Thusfar we haven't had any trouble with predators. Ironically the only thing that's ever gotten one of our girls was a hawk when they went in the open yard and my neighbor's dogs.
They are quite happy and healthy and find all...