I think the only real solution would be to have fully netted, screened wired areas that keep the chickens within safely and the eagles out. It may not be entirely free range, but it would eliminate the eagles poaching and all the ramifications that.
They say that they move the chickens huts every so often. Why not make it so that the enclosure and the huts can all be dragged to a new location (at a slow speed) without ever having to take the chickens out or in. Make it sort of like the circular farm irrigation rigs that turn in a large circle. A full screen/wire/nylon enclosure wouldn't be any heavier than that.
English
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That would probably be a pretty solid solution. One guy in the comments also suggested livestock guardian dogs, which they apparently have a few, but they don't ward the chickens nor are they trained to deal with eagles.
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Too many eagles and they're too fast for dogs. I've seen vids of eagles taking down deer, even on a full run. Dogs would just be minor irritants to them.
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Damn, those eagles don't -blam!- around.
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Nope https://www.youtube.com/watch?v=D1u438JAOSo