I have experience with LGD's and the dogs I prefer to use with poultry. When is comes to use with poultry, the treatment of dogs is the same regardless of breed. Imprinting works well with herding animals that move about landscape but such does not provide advantages with chicken flocks that are sedentary in that they seldom range over more than a few acres. I have employed imprinting with other dogs breeds now and it just does not provide the advantages needed for dispersed chicken flocks that are targeting by predators that employ the snatch and run approach. The dog simply needs to guard the location and otherwise leave your stock alone. It can respond to chicken alarm calls which for my dogs that is standard. Not everyone will agree with your assertion about GP's thriving in a small area. With really small areas of a couple of acres or less other non-guard animals tend to be more cost effective unless the guard animal has other uses.
While the treatment of the dogs may be the same, the response always isn't. You could very well lose some of your flock to your own dog when not watching. That's unlikely with an LGD. I too had a different shepard mix here once. She was set to make lunch out of my flock until she received a hard lesson. She didn't touch them after that , but she sure didn't protect or guard them either. I was still losing birds with her around. Coyotes were even snatching and taking several off at a time. That does not happen anymore with my LGD.
That fact that chickens are sedentary and don't roam much actually makes it more ideal for a lone LGD. With a smaller area to watch, she is able to keep an eye out on all the different bird groups. Now, if you are saying that your LGD will follow the sheep out to pasture and leave the chickens alone around the barn, yes, if you have multi livestock and huge acreage that can happen if she is raised around the goats. But, OP only has an acre, so that's not likely to happen. Just as I only have a few acres and only chickens, no other ranging animal. Even though I have a few unfenced acres, the dog stays here where we and the chickens are. They simply aren't energetic dogs and an acre is actually pretty large for a sedentary animal. Large enough for a single Pyre. Will the dog go beyond the acre if able? You bet. Just like any dog would. But they will not stray far from that they are imprinted with. Is it easier to lose a chicken here and there with an LGD as opposed to a goat? Well yes, because it takes no time at all for a chicken to be snatched. Although, my dog did save one of my chickens from a hawk that had her down. But overall, they do their barking and keep many predators away. I think I have only lost two birds in the six years I've had my dog. One to the neighbor dog while she was still young and untested (this is the episode where she really matured and understood her purpose) and one to a sneaky predator near the edge of the woods. So, nothing like what I had been experiencing on a yearly basis where I was losing most of my birds
.I really don't understand your cost effectiveness deal unless you feel it's just cheaper to replace your barnyard type chicken. That's likely true and if people don't get attached to their birds, it is cheaper to just replace the birds every year. However, if you feel an attachment to your birds or you have pricey breeds you raise and you want to free range then a guard dog makes sense. The LGD doesn't require any more food than a sixty pound dog and much less than a dog that size that is highly energetic. You know how much my dog eats a day? Barely over a coffee can full of dry mix. Quality meat based food, not the filler type cheap stuff. That's another topic though.
Now if you are talking about the price you may have to pay to obtain an LGD, as opposed to a pound puppy, that's a little different, but not impossible. A shelter dog will cost you roughly $50 to pick up at the pound unless they are having a special. I found mine through local newspaper ads for $150. I have seen people ask as much as $500 and I have seen them for as cheap as $50 each at times. Usually when someone is trying to sell the last of the pups born every year. You can usually get the LGD crosses for these prices, like an Anatolian x Pyre mix which will probably be my next choice when I lose this one.
I am very happy with my dog. My neighbor was very happy with his and had similar circumstances. My other neighbor not as much, but I'm convinced it was their training methods to blame there. The raised their LGD with a mutt and that's who the dog bonded to. A chicken killing mutt at that! Their LGD didn't kill the chickens but the mutt did. So, it is important how you raise and handle these dogs, as with any dog. It's head shaking to read on this forum alone those topics "my dog killed my chickens". Well, duh. It's what most dogs do. Sure, some dogs can be raised up with your chickens and leave them alone, but not all dogs are protective of their territory. That's when your chickens will be in danger from other dogs and predators. Because that dog just doesn't have the "it's my territory" get out of here mentality. You know those types of dogs exist. They pee when they see you. Or they are friendly to a fault. They welcome everyone! They aren't going to stop an attack on your flock. So, while you can get your dog to accept your chickens, you really don't know what you are getting as far as "protective" or "territorial" instinct.
One other thing. The problem with a "territorial" dog for some people will be the liability they can be exposed to. If you live way out in the country, there may be no problem. If you socialize the territorial dog, there may be no problem. But, territorial animals are not always friendly to people. That was a huge concern of mine when choosing a guard dog. I'm not fenced, as most people with some acrege aren't. I can't risk a territorial dog attacking somone walking down the road or making a delivery. When researching breeds, that was #1 on my list of priorities. Maternal, protective instinct works much better for me than territorial.
