Welcome to the forum!
Glad you joined us, just wish it were under better circumstances!
There are different things that could be causing that. Each flock has its own dynamics due to the personalities of the chickens. A few thoughts.
Are you sure they are killing and eating each other? If one dies, especially if some meat is exposed, they will eat each other, but are you sure a possum or something like that is not getting in the coop and killing one? Different predators have tendencies, but not all possums, raccoons, weasels, minks, bobcats, whatever will act the way you would expect. This kind of sounds like a possum, but it could easily be something else. For example, weasels are known to kill a lot instead of just one and eat the heads, but you never really know. This is what I really expect is happening, but you are looking at it and I am not.
My next thought is space. Your coop should be big enough for that many chickens, but each flock is different. And the longer they are kept in a small space the more likely you are to have behavior problems. It's like they get bored and start picking on each other, like cabin fever. I know you are a lot further north than I am and you get more severe weather, but you might try giving them the option to go outside, regardless of the cold. If they don't want to go outside, they don't have to, but you might be surprised at what they choose. Mine choose to go outside on my coldest days of the year, which is around 0 degrees Fahrenheit. Mine don't like a wind, and they don't like snow at first, but I've had some get used to snow and go out foraging in it. Chickens normally do quite well in cold as long as they can get out of the wind. I suggest giving them the option.
Another thing you can try is toys to break the boredom. Try putting in a few extra perches or maybe things they can hide behind. Another thing is to hang a cabbage so they have to work a bit to jump up and peck it. Throw some Black Oil Sunflower Seeds on the floor for them to scratch and find. Just something to break the monotony.
It is possible they are short on protein. I put this last for a reason. If you are feeding them a balanced diet, this is probably not it, but upping the protein a bit won't hurt them. The Black Oil Sunflower Seeds will work well for this.
With it being as regular as it is and with the injuries you describe, I strongly suspect a predator. But with chickens you can never be sure.