I think an electric fence is a good solution. It's worked for me in the past. The only other sure fire predator-proofing method is a solidly-built coop and a run with a top, preferably made out of turkey wire and/or hardware cloth (even a small determined predator can tear chicken wire, and since I live in the South too, I know how fast it can rust). And you need to bury or firmly anchor the bottom edge somehow. I've done it both ways, bury it a foot deep and/or flare it out and cover it if I can't dig deep, or line the bottom of the pen with landscape posts and nail it to them. I know a lot of folks don't like salt-treated lumber but I don't know any other way to keep it from rotting or eaten by termites, especially here in the South. And your electric fence could help here too. You may not be able to keep as many birds because building a big pen like this can be expensive, but I'd rather keep fewer and have them healthy and safe then keep a lot and always be losing some to predators. I occasionally let my birds out to forage but most of the time I keep them penned. For me hawks are the worst predators. And domestic dogs. Again I know a lot of folks will disagree with me and I respect that, but I'm not above applying the 3 S's when it comes to predators - shoot, shovel, shut up! But you have to actually catch them in the act to do that, and most of the time they come when you're not around. Prevention is the best remedy, even if it means keeping fewer birds.