Have you ever planted vining okra ? It growns like crazy, like cucumber vines, flowers like okra and make pods that are rigided, you can eat them when they are small or let them grow, dry them out, rough up the outside of them with a butter knife and they are like loofahs.
I have half buried tires in the run and am going to plant inside w/ vining or vining type plants (malabar spinach, cukes, squash, indeterminant tomatoes etc...) then encircle the planted tires w/ sturdy wire fence ( the stuff they put in concrete) planted in sets of 3 tires w/ space between them then topped and connected w/ the same wire. The plan is the plants will grow up and over the wire making green shade for the girls. They won't be in these runs until after it gets really hot (the last of June or so) so the plants should be good and big both for shade and so they can't do any serious damage by pecking at whatever leaves they can reach. That is the plan anyway, this is my first attempt at this so we'll see how it goes.