Many thanks for your kind words. It's great to hear back from people who are as excited as we are about working with all these great tools. As you say, they are way under-utilized.
In terms of the site, it's true that we don't make the lecture source files and all the code that generates the site public. One reason is that we'd like to eventually publish a hard copy version of the site through somewhere like MIT or Princeton UP. (I think that will help with adoption in courses.) Publishing would be a bit more problematic if all of the source was open.
The lecture site started as a very basic static site, built, as you say, with Sphinx. The theme we used is called f6:
We're very lucky to be supported by the Sloan Foundation and we have great postdocs and research assistants (particularly Matt McKay, Chase Coleman and Spencer Lyon), as well as some input from a web developer (my brother Andrij Stachurski). That's allowed us to get a nice looking front page, the two versions of the sites, nicely compiled PDFs and so on. (The two versions of the site also involve some Jinja templating.)
But even without all those add-ons, you can go a long way with just a straight up Sphinx site and a nice Sphinx theme. That will already produce a static site and lecture pages that look similar to ours, including highlighted code, latex for equations, etc. If you know a web developer they can probably customize the theme to fit your tastes (colors, margins, etc) very quickly by tweaking the CSS file that comes with the theme. Hopefully that alone will get you to a site that's suitable for your course and that you're happy with the look of.
Please feel free to ask further questions.
All the best, John.