I'm just seriously surprised your ok with letting your dogs wander O_o
The thought of disease and death does not seriously worry you? One bite from a rabid disease ridden raccoon and poof there done.
On the topic of it finding a dead bird without any insides. It is very possible a local neighbor could be trying to get rid of a bothersome raccoon, coyote, or even very possibly your own dogs. Even though it is illegal it will not stop some people.
Story time, my neighbor up the road had a lab, hound cross, and has a lot of property.
However, he always let the dog out off leash because he felt the dog would not hurt anyone or go far.
The dog was cute and he was right, it never wandered to far or hurt anyone, it just loved to play with the beef cows. Literally they played in the cow field.
Then one day the dog went up and tried to play with the dairy cows...As you can guess that did not go over big with the owner when they stressed and flattened one of there own in the scramble.
The farm owner warned the guy multiple times.
And he just kept saying "Don't worry she wont hurt no one, she wont hurt no one she never goes far"
No, intentionality the dog did not hurt anyone or even go after anyone. It was used to playing with the beef cows.
Well, after the...I think it was four times the farmer complained, the just dog vanished...Just flat out vanished and no one can prove what happened or didn't happen.
True story, I liked that dog, and now shes gone.
If you cant see your dog, you can not protect or save your dog from what may happen. All it takes is a second for an accident to happen.
If you still want to let your dogs out off leash/fence, i would walk to all of your local neighbors and let them know about your dogs.
Let them know that if there is any problem that they are to call you directly, and give them your number. This way you can monitor there actions should they wander to far one day, and this way if they do cause trouble you will know about it and can then make the decision as to what you want to do. Leash/fence/pen them, or continue to let them out and just non stop monitor there out time.
I would still never be able to let my dogs out off leash, not after dealing with so many rabid, nasty, diseased things...
But I hope this may help!