I would be setting out traps in my case if I didn't have 5 barn cats that I don't want to hurt!!
First, I'm very sorry for your loss. I always hate to see a new post of someone losing their flock.
A game camera would go a long way in helping you know exactly what you're up against. As far as traps, if you use large havahart style traps I believe your barn cats will learn to avoid them after being caught a few times. They're just one part of a comprehensive predator defense though. Best of luck to you!