I just took some time to read the nice blog post at http://blog.beeminder.com/write
What about integrating Overleaf (online LaTeX editor) in the same way as drive or dropbox? That would be super cool!
Or, I’m just asking for something that already exists?
Indeed, Overleaf provides urls for projects.
Another comment on the side: please let choose between word count and characters (keystrokes) count. In EU we’re not very used to word count (instead, something like 2500 keystrokes, spaces included, is somewhat equal to one page of text).