Livestock guard dogs, as you mentioned, may be your best bet. They are actually pretty easy to find. No need to look strictly for Anatolians. They are great dogs, but so are Pyrenees, Central Asian Shepherd, Kangal, and any number of other breeds. A quick search on Hoobly will find lots of them. Look at people breeding that actually use their dogs for their intended purpose. Don't shy away from mixed breeds that are two or three different LGD breeds. Many people mix them. I did a quick Hoobly search to give you ideas:
LGD on Hoobly I searched Livestock Guard Dogs. You will get a lot more hits if you search individual breeds. Best of luck to you.