I am not sure if it’s in the best taste to answer my own question but, after a bit of work, I put together an app that solves the problems in earnest: django-hitcount.
You can read about how to use it at the documentation page.
The ideas for django-hitcount came came from both of my two original answers (Teebes -and- vikingosegundo), which really got me started thinking about the whole thing.
This is my first attempt at sharing a pluggable app with the community and hope someone else finds it useful. Thanks!