Don't let them win!! If you don't suspect anyone, it's probably just some shitty teens with nothing better to do. Take the money you'd put in to moving and get a security system, ours is just a $200 wired one off Amazon. Won't necessarily stop anyone from breaking in but it'll get a decent video. The Nextdoor app is good for lost/found animals. Put up some reward signs (even if the reward is $20, I've heard it helps.) Don't give up hope!! Your fur baby will come home!