Based upon the way my cat kills - and how she accesses the pens, she's too small to kill my poultry - stunted cat is about the size of a rabbit, but kills anything smaller than she is, I would vote fox. Cat isn't going to chew fences. When they come up against a challenge they prefer to climb, and there is no fence that will stop them. You'd end up scalping your property bald trying to get anything that could be climbed and jumped from away from the pens.
When our cat kills something, she eats the head first and then uses her scrapey tongue to remove the undesirable bits from inside. She dumps them out like a kid with a bucket. Amazingly efficient, takes under a minute. Then eats everything else, bones included. If she leaves anything it's the hind quarters. I'd look for gut piles if I really suspected big cat and then I'd have to take away yard access and put everyone in somewhere that couldn't be accessed from above. Full overhead cover and hope they loose interest or find easier targets elsewhere. For the big guys to come in, it means the easier hunting is gone and they're pretty hard up, unless they've already been hitting neighboring farms and have run out of easy targets there and are just habitual human herd hunters, and that's one to contact fish and game about.
It takes time to chew things and cats aren't going to spend that time when they have the ability to go wheee!
Foxes are sneaky chewers though, since we have yotes, we don't have much big cat activity -they're on the other side of the valley and prefer the neighborhoods for garbage, dog food and small dogs - they don't seem to fear humans the way the coyotes do. They don't seem to be bothered by suburbia.
Dew lines of course might give you a direction and a general idea. When we get bigger predators, it's along the same track - they pass behind our property in the night or early hours of the morning. If you got their routine you could wait for them and give them a significant unpleasant experience, then follow up with a light on a motion detector. You can get a screw in that goes between the socket and the bulb at a hardware store for around $40.
Sorry to hear about your losses, hope you get the perp or get your coops secure before they get anymore of yours.