These cats are driving me INSANE...!!?

Wow, you do have a problem there, but the answer might be rather simple. You let Smokey (your cat) out to eat gr and whatever? You also say you run an AC to drown out the noise of cats in your backyard. Why don't you keep Smokey inside for a week or so.? You won't hear anything. If he's not outside, these annoying cats will have no reason to congregate in your backyard. They'll hopefully go somewhere else and you'll be able to let Smokey enjoy his backyard again.