Is there an app that will show me total word count across all applications over a period of time?
Mac Word Counter should help you.

From the above-linked splash page:


  The Word Counter …
  
  gives immediate feedback on your productivity as a writer.
  
  encourages you by showing you your daily output.
  
  gives you clarity about your daily goals.
  
  keeps a complete history of your daily achievements.
  
  assists with finding your perfect writing environment.
  
  counts what counts: words – the ultimate metric for writing.