One of the more common posts on nextdoor.com is about missing pets. There is some degree of success with finding the pets too. I live in suburbia though. I don't know how well being in the middle of the sticks would work though. It still wouldn't hurt to post there then try the police.
The big problem with nextdoor is from reading the posts, you find out how hurtful and ignorant the people who live around you are.