Similar problem here, but it was a rat. The thing was a frickin genius. The balls on this thing. It would run right past you. It ate my daughters shoes and a couch in the guest room. We tried everything. The exterminators said they had never seen that kind of damage from a rodent before.
Went to PAWS and got the biggest cat they had available. I asked if it came with a saddle. I’m talking big cat here. The rat vanished. Still have the cat, and we do what ever he says.
LOL! There's a video on YouTube that shows a rather small cat killing a good-sized rat. It's a disgusting video, but absolutely fascinating. The cat corners the rat; the rat tries attacking the cat, but the cat eludes it every time. Then the cat sits in front of the rat and repeatedly bats it upside the head until the rat has been knocked silly; it then seizes the rat and eats it. It's neat to see how deliberately the cat lifts its paw and takes aim at the rat, and gets it every time!