I'm pretty sure C2 (Or maybe the browser itself) does something internally to *stop* what you're trying to do, from happening. Basically, if it's a different C2 project, it won't read/write to webstorage values from another project, even if they have the same name. It makes sense when you think about it in the context of browser gaming - if I'm playing 2 different games at different times in the same browser, and they both have a key called 'score', you obviously don't want that value to conflict.
In order to do what you're trying to do, you'll either need to find where NW is saving the values (I haven't looked into this, I think it's somewhere in appdata) and do something with that, or, you'll want to create your own save file using the NW plugin's file i/o features, and monitor where users are installing each 'episode' so they can all access that file.
There's probably another way to do it, but those are the options that first come to mind.