I clipped the Primary flight feathers on one wing of my hens and they stay in a 4ft fence (it may be closer to 5 ft I am not sure) I have Golden Comet hens. If you click on the photos to enlarge you may notice the welded wire run near the metal chicken coop (hard to see I must admit).
We have movable paddock fences that are four feet high. To keep the girls in and the hawks out, we put deer netting over the top of the paddock. Deer netting can be purchased at any home store and is fairly inexpensive. It takes two people to do it as the netting will catch on everything and is a pain to work with. We just lay it over the top of the paddock and then secure it to the sides of the paddock fence with zip ties. We will also use zip ties to keep the netting together where two pieces meet.
It's not beautiful, it won't keep serious predators like raccoons out, but will keep out hawks and will keep chickens in and it's cheap and quick to do. Hope this helps.
Yes, cover the run! I use shade cloth, but you could use deer netting. My chickens escaped every day until I did this. I only let them out of their tractor when I am home, and during the day. Come evening, back into the coop they go. I so feel for your stress! never knew chickens would be so worrisome!