I was thinking coon also...I'm not sure why you keep sending your dogs out to be hurt. I would have used the trap. That gash could have used some stitches. I'm not saying this to belittle you or tell you what to do, I'm just a little confused.
These are guardian dogs, doing there job, there absolute purpose in life is protecting the OP's pastured animals, it is what they are bought and kept for, and can take much more beating up than say a chicken, or goat...........
They would be very unhappy dogs if they were kept locked up until the predator is caught. Alot of people would say the same as you, but for those that know these kind of working dogs.
4 large dogs could easily kill a cougar, or even a bear if they are threatening there charges anatolians (SP) were once known as wolf killers I think.
I do not however think either of these is the culprit, I'm seriously thinking a coon who is escaping though the fence..