I ended using Jekyll with Martin Fenner's jekyll-pandoc plugin. Jekyll is a static site generator with blogging capabilities and a built-in templating language. So you get the best of both worlds from dynamic websites (no redundant content for navigation etc.) and static websites (no dependency on a databases, no scripts running on access).
The jekyll-pandoc plugin is necessary because I want Jekyll to use Pandoc for converting Markdown to HTML. The Mardown renderers that come with vanilla Jekyll do not support references and other stuff you would expect from Scholarly Markdown.
I had installed Pandoc already when I converted the project proposal from LaTeX + BibTeX to Markdown. When using Pandoc, be sure to get the latest version because it really is the greatest.
For usage statistics, I will feed the pseudonymized logfiles into AWStats (because the logfile importer for Piwik is currently broken/too slow, and Piwik itself is too slow anyway).
This setup fulfills all the requirements above. I would love to see alternatives which can do this, too.