Have you considered keeping them in a coop/run setup? I'm in the piney woods North of Houston and have a ridiculous amount of predators that want to eat my chickens. I built a large predator-proof run attached to the coop (including a hardware cloth skirt to prevent diggers). They're happy and healthy. I even have a "chicken tractor" so they can graze in the grass without risk of predators.
If you love your girl and are considering keeping her and getting a couple more so she's not alone, this might be your solution!