Do your private posts have a post type? If so, the reason the post type isn’t showing up in the Post Types to Publish setting (found on the plugin’s Publishing tab) is probably because of this:
It is only looking for public post types. You could try hooking into the discourse_post_types_to_publish filter and adding your private post type to the $post_types array.
The best practice is to use an available action or filter hook and make your modifications in a separate plugin. If you need a hook added to the plugin, just ask. My goal with the plugin is to make it as extensible as possible.