Toni we have a neighbor who takes in feral cats, catches them, gets them neutered. At one point she was feeding 70. (She has a 5 acre yard.)The other neighbors complain bitterly about all the cats around scaring off the song birds. We have loads of song birds in our yard...and no cats. Our two dogs love cats, but they love to chase them. so the cats stay clear of our property. Maybe you should borrow a dog from someone!
I've noticed the past few months that numbers of both cats and rabbits have decreased. I used to see dozens of them if I drove in after dark. Now I hardly see any. Wonder if the packs of coyotes I hear each night are feeding on them? could also be a hawk, eagle or wild boar.
Zuzu, can you buy predator snails where you are? What about diatomaceous earth? Or a hungry chicken?