Glad to know it's helped solved your problem.
I think you could still use tiled backgrounds. In the left properties bar, in the hotspot section, make sure it is set to top left. It might not be as perfect as using sprite with its image point option, but it could still work. If you add some clever objects on top to hide the main hotspot where the chain turns, you could still get nice results.
I've created a new example with what I mean, so hopefully you might still be able to use tiled backgrounds.
https://www.dropbox.com/s/y412q5jehlplxpg/DogAndChainExample2.capx