Add the online preview's theme customizer (or other sections) to the sidebar
In order to add the online preview's theme customizer (or other sections) to the sidebar we've created a separate plugin for the customizer and you can download it from this link. It's pretty easy - the php file outputs the content inside the sidebar, while the css & js files control it's style / behavior.
You could start from this and do whatever you want i guess. Just note that i cannot give any assistance with this custom work.