I have a similar situation to you. I mostly work at home, have cats and dogs and have pastured chickens. I have large fenced pastures that they stay in (I have 3 different flocks now in separate coops.
I have had chickens here for 2 years (have lived here for 2.5 yrs). I have some grass around my house, but we are surrounded by woods. The critters we have seen are fox, raccoons and hawks. I know there is a coyote in the area as I saw it on one of my walks with my dog. I use my dogs as predator control. Dog goes out first thing in the morning and ranges around the yard into the woods. Every time I go out, dog goes out too. We definitely had more fox activity when we first got here--I heard the vixen's call several times/week at night. Every time I heard it close-ish, I took the dogs out and sent them into the woods. They got to the point that if they heard a fox, they asked to be let out.
My dogs are very well trained and can be called back when I decide they have gone far enough. If I had a fence around the whole property, I'd let them do what they wanted lol.
I have had 3 hawk strikes with 1 loss and 2 injuries. All issues were during the migration--once in the early spring, and once in the fall. I have a rooster and I believe he helps. He does watch the skies and calls his girls to cover if he sees something. The loss I had was in a pen with no rooster and an injury was to a young roo who was small. I know what the upset rooster call sounds like (sort of like a manic egg song) and the dogs learned to recognize it too. We all go bolting out the door if we hear it.
I think my dogs keep the land based predators away. Though last week my husband peeked out the window and said "I think Stripe (cat) is chasing a fox up the driveway". Sure enough there was a fox with in 30' of my young chicken pen with the cat trotting after it up the driveway...Maybe the cats keep the predators away too lol! Not sure if the chickens or the cat was on the foxes menu, but me and the dog finished chasing it away.
I have predator proof chicken houses and the ladies are locked in at dusk every night and out after full light in the morning.