I grew up 'summering' on a lake not so far from you, long ago, and love the area!
You will never eliminate every predator out there, and it's best to spend most of your efforts and $$$ making a predator proof coop and run. Where you live, that includes electric fencing for those black bears!
With perimeter fencing, livestock guardian type dogs can be a big help, but they take time (years!) to raise and train, and are the very most expensive option of all.
Here we don't have bears or cougars (yet) but we do have every other predator that you have, and also free range our flock whenever possible.
Raptors will visit, and then the flock needs to be in their safe coop and run for two weeks at least, until that bird moves on elsewhere.
Our worst one day predator attacks: One day, a mangy fox killed ten nice hens, seen by a visitor next door, and no help there! The, last spring, our fencing failed, and one of our own dogs killed two dozen! That was awful, and due to a fencing failure with a dog we know isn't safe with birds.
Having a safe coop and run prevent many disasters, and sometimes that might include eliminating a persistent raccoon, fox, or opossum, but since having no food outside of their safe zone, and locking them in at night, most issues can be managed.
Some folks have more problems than others, some birds are easier targets, like bantams, youngsters, and Silkies, and some people don't free range at all because of losses in the past.
I'm rambling on too much!
Shooting every fox or coyote you see at a distance won't help, short answer.
Mary