Many people using SNAP for a long time, and it can be challenging sometimes to isolate issues with this particular plugin. However, it does seem obvious that your Featured Image is possibly implemented differently within your theme.
Does it post the Featured Image to the other sites without issue? If so, this often indicates there might be a problem with your SNAP configuration relative to FB.
Are you using JetPack's image CDN program? If so, there could be some internal confusion from the plugin about which image to use, and so it would default to your pre-set fallback OG:image.
Perhaps your url shortener is causing the issue.
So on and so forth in the process of troubleshooting.
Shoot me a PM if you want, and we can try to sort this out via Skype or something.
What you will find with most auto-posters is that at some point - you need to learn to troubleshoot these issues because they are almost inevitable with all automated mechanisms - particularly those automated by way of complex database driven solutions such as wordpress installations with mixed plugin configurations. There are many things that can cause a problem, so it can often be difficult to isolate. Nonetheless - all these issues can be resolved with consistent attempts to resolve them, so I recommend fixing these problems rather than running to another solution.