Hi James,
Even though you are viewing your story through your customized app you should still be able to edit the story content using the builder that's hosted on ArcGIS Online.
http://dcgis.maps.arcgis.com/apps/MapJournal/index.html?appid=221d5bffdd61468b8463d67b1b2d596d&edit
If you want to use the builder through your customized version of the app you'll need to register the app, get an oAuthAppId, and add that to your index.html.
When you mentioned you "registered" your app what you did was just add your app's URL as an item, you still need to go to the Settings tab of its item page and click Register at the bottom of the page. More details here: Add items—ArcGIS Online Help | ArcGIS
Let me know if this helps.
Owen
Owen Evans
Lead Product Engineer | StoryMaps