If you have this big of a flock, you need a LGD. No way around it.
If you live in a rural area with no neighbor's pets nearby, this is an old family recipe. Day old donuts, soaked in Roundup. They are indiscriminate though. It wouldn't be worth it to kill a neighbor's dog or cat.
I have tried leg traps and they just are a pain to use. You need to be strong and fearless! If you go this way, when you catch one, pick up the entire critter and trap and drop it into a trashcan full of water, then donate the carcass to a zoology college department. The drowning preserves the carcass for dissecting.
This sounds pretty harsh but this is the price needed sometimes.