That’s what mine do whenever they see a shadow. They also usually don’t leave them selves exposed out in the open, they sort of go from tree to tree.I feel for you. I'm also in Washington state, and the eagles are especially prolific this year. I free range in my orchard as well and lost my little call hen last month to a giant bald eagle. Came right up next to the house to get her. I witnessed three additional attempts at my standard ducks down in the field, but was able to run the eagle off before any casualties. I know that they're beautiful and it's nature and all that, but I really wish we were allowed to treat them like other predators.
You may have a different experience, but I have never found reflective tape to be effective against aerial predators. The only thing that works around here is plenty of cover. I have a ton of river willow and weeping willow trees that the birds take to when they see a big shadow. We are also currently in the process of building a much larger coop so that we can keep them shut in for a week if necessary when the eagles are particularly bad. I say to give your tomato cage idea a try — I'd be delighted to hear if it works!