If Story is not published, these custom templates will not appear in your template drop-down list.
This occurs when you are working in the non-published theme. To solve this problem create a page template of same name in the currently active, published theme. Then the page template will appear in the non-active theme.
After selecting the page template style and saving the page settings. Return to the Online Theme Editor and navigate to page which has the assigned template.
Use the Customize button to start the Theme Editor