Not sure what your run is like, but we got an electric fence because we have a lot of wood's around our house, and to keep the hawks out we ran fishing line across the top. It has worked really well! We lost one to a hawk also, but since we installed the fishing we have not lost any more! YA---HOO!!
I guess I am not sure what you are saying, do you put fishing wire high in the air, what test line do you use? How far apart? and does it knock them out of the air?. I used to have 2 Jack Russell terriers in my chicken yard, but the hawks got 1 one day, and then 2 days later, he killed the other. What a sad sight that was with their eyes and head all eaten up. I have seen cats carried off and eaten by them also. We used to have lots of pheasants all over the country in this part of the U.S. but not anymore. If you see one, you are really lucky. I still see lots of cottontails and jackrabbits, but no prairie chickens or pheasants. Maybe they will change the laws so we can protect our livestock again.