My biggest problem is also dogs, but not wild dogs. It’s dogs that have been abandoned in the country.
The best protection is barriers. Fences that keep the dogs out. That’s hard if you free range them but electrical fences and electric netting can be very effective. I use electric netting for that but if I had to do it over I’d probably build a fence and electrify it.
Your next most effective is a trained livestock guard dog or two. They need to be trained so they know what they are supposed to guard. They also need to live out there 24/7. They cannot be brought indoors because it is dark outside or they might get cold. Many LGD’s like to patrol too. It’s hard to give them the freedom to do their job and keep them at home all the time.
I don’t put a lot of faith in llamas, donkeys, or such. Yes, some will attack canines when they see them. Some won’t. But the main reason is that llamas and donkeys do not bond to the chickens. They don’t attack foxes, coyotes, or dogs to protect chickens, they attack, when they do, because they don’t like canines. There is a donkey in the pasture across the road from me. I’ve seen a dog walk by and that donkey ignore it. There are also cattle with calves in that pasture. I’ve seen cattle at one end with a coyote not that far away. The donkey was in the far end of the pasture providing absolutely no protection. He did not bond with the cattle either. Will animals like this provide some protection, yes, but not a lot.
Trapping and shooting predators will reduce predator pressure some. It will at least get rid of the animals currently hunting your area, if you can get them. It’s hard to get them all to start with. And there are always others ready to move in. At the best it is a temporary solution.
In my opinion your best bet by far are barriers. Other things can help, especially a good dog or two, but barriers are by far the best defense.