I can't find it if there is one, but it'd be great to have an example site.
There is none and I don't plan on creating one. I understand why you want one but I don't want to bother with hosting a dynamic website that I would have to manage. (Rather spend the time improving the app itself.) I include a screenshot and an example is wookmark or pinterest's websites. It functions like those. If you want a demo of this exact app then clone it and run it. It's free and open source!
Out of curiosity, after once deploying it, what're some responsibilities that entail from hosting a dynamic website vs. a static one? Isn't it basically a matter of writing (/copying a good one and retrofitting) a fabric script, perhaps doing just a few things with some Apache/nginx config files, and just putting it up? What exactly makes it more hands-on post-launch?
I had been under the impression that this process would not take more than a few hours by itself.