Miss Red - First, I have to side with you on what you did with the cats. They had a taste of blood and chickens and they would just continue to do what they had done if they could get away with it. Let's be serious, folks. Shelters are FULL of cats and dogs and whatever that people don't want to take care of because there are WAY too many irresponsible people who do not get their pets spayed and neutered and just let them breed rampantly. AND since when is it INhumane to shoot an animal? Do you really think that boxing or caging and animal up (which really freaks them out and causes loads of stress) and taking it to a vet to then handle in a strange environment so they can wrestle with it, holding it down and making it even more afraid and stressed, just so they can inject their death through a needle is more humane than the quick, unexpected shot of a gun? Give me a break. I love animals, and I have a hard time putting down those that need to be when they are sick or injured even, but I do it in the quickest way I possibly know how and don't make them suffer or try not to make their last moments any more stressful than they need to be.
If I had been in that same situation, I would have done exactly the same thing.
Now, as for the mess you came home to, it wasn't just those cats. I know others have said it, but that was the work of a canine, leaving that mess strewn all over. Blue didn't do it because he would have feathers all over his mouth and there would be no survivors or at least none huddled anywhere. The go into a frenzy and kill them all. Poor Blue sounds like you have trained and he has understood exactly his place and is protecting your birds. Somebody else came in and did this. I would be tracking them down, and if it is someone's dog, I was expect compensation for losses. When it is your livelihood at stake, the rules are pretty clear in my book.
AND I am so sorry you lost your birds. I know that sick to your stomach feeling well when you find that mess. It is heartbreaking.