Another half an hour of work later, and this site is now run by a static site generator, with the site updating via a Git hook. Given it was effectively already run by a static generator but without the "static" bit, it was a small jump to just get it to spit out a set of HTML files.
It's not entirely efficient but it works, and will probably make the site ever so slightly quicker. Yay!
Also gives me the ability to churn out pages that don't exist as actual posts, such as the tag pages on the Blog page (such as the Site tag). That is where things will start to get more interesting.
Makes you wonder why I didn't just install Jekyll or something. 😩 But this is much more fun!