Unfortunately, that's not how JFBConnect works right now. We'll look into adding that functionality, but I can't guarantee we will. I don't think your usage case is the most common, and we need to make sure JFBConnect works for all usage cases.
As for the Like button in general in the category view, when JFBConnect adds it, like I mentioned before, the button will always point to the 'final' destination URL for the article, not the category view URL of the current page. Are you using the JFBCContent plugin to automatically add the Like button? If so, then I still think it should use the final article image. If not, let us know. If you're using a custom button on the page though (for that category URL), then that would be another indicator that you'd need some way to specify the Open Graph tags manually as well.
Hope that explains,
Alex