Oh, Hon, I am so so sorry. If you're ever in the neighborhood you're welcome to some of my Orps anytime.
You're right--this was THEIR irresponsibility. Please don't beat yourself up about it too much. You'll feel SO much better once you get a good fence around your place, and yes, they'd do it to other livestock, too. I've had neighbors' dogs even get into pastures and chase HORSES. UGH. And since we value our dogs, we just don't want other dogs, with a risk of brucellosis and who knows what else, to even set FOOT on our property, regardless of whether or not they do damage.
A gamecam is not a bad investment. Not only to "catch" wild predators so you'll know what you're dealing with, but in case you ever need PROOF when someone says, "Oh, it wasn't MY dog."
I like the paintball idea, too, though I've yet to try it. At the very least, it sends the dog home with the distinct message to the owner that the dog's been somewhere it shouldn't be.
Again, I'm so, so sorry. Leash law or no, keeping your dogs up is just common decency, as well as good animal husbandry. Loose dogs make me see RED. Ironically, on our street, the most menacing loose dog is a Great Pyr who the owners maintain must be free to roam in order to fulfill his "livestock guardian" duties. Grrrrrrr.