Josie I wish people had the nerve to just come up, knock on the door and discuss things like adults. I've had people a mile away comment about my GPs barking on quiet nights. No open complaints though. Last night my own dogs kept me awake. Predator level is so high right now.
If you know who it is, or have a good idea, I would simply go be very nice, but explain they are there to protect your livestock and they do so by warning barking. Say that you are sorry that it disturbs them but that it is because predation is so high right now. That once the predators move on the dogs will be quieter.
Maybe offer them a small peace offering like some cup cakes or something as a friendly neighbor gesture to help sooth them.
If they react hatefully I'd be calling the sheriff again just in case, to see if they will prosecute if one of your dogs gets shot. Not that that would help the way you feel any but after being there I'd want to know you could prosecute if necessary.
Meanwhile if it were me I'd be thinking... "close your windows, insulate your house and buy a white noise machine to muffle the noise. "
Some people would rather complain than just learn to deal with things.
King Bee doesn't that just make you dislike people? I am still angry that someone chased my dog down and shot her.