I'm so sorry about what happened to your birds. I have a reputation in my neighborhood.
10 years ago I had a very similar incident on my farm. I borrowed my Dad's 4-10 and put a total stop to it. In fact, now I am known as the lady that
will shoot your dog! I love dogs, it was one of the hardest things I've ever had to do. I was really concerned that one of them might attack my 4 year old grand daughter, or my other beloved pets.
Now everyone on our road keeps their dog on their own land. I have dogs as well, they are well cared for and I keep them at home where they belong. The best way to get them is to set up a trap and blast 'em with a 4-10! My 4-10 does not kick, and it is very accurate. Borrow a friends shotgun, or find one and waste those killers, before they hurt someones children.
Don't bother digging a hole either, just throw them on the side of the road.
It might sound cruel, but a pack of dogs can be dangerous. More than likely they have not been vaccinated for rabies either.
I hope you get them soon!