What about making a chicken tunnel?
Due to cost restriction, you may not be able to given them the entire orchard though.
I'm picturing hardware cloth or welded wire fencing. Chickens are under 2' tall, so you could buy a number of 8' to 14' 2x4s, cut them every 2', to run the fencing across the top of.
You could choose to box in the sides or not. Even just doing a long strip of this wire supported by timbers (or bricks, stumps, suppose anything works) would give them a large area where the nasty buggers can't swoop down to grab them. In theory, they should still feel free and carry on business as usual.
My orchard can fit the tractor down each row, can yours? Making this tunnel in the big open row plus maybe adding a few other objects to hide under might help. I don't know if eagles will swoop down and then attempt to retrieve a chicken from under an object...maybe someone else knows. If they won't, you could use pallets leaning together, pet igloos or carriers, a trailer, etc.