Are you thinking of some kind of hybrid system, in which there's a Disqus-like web app to serve recent comments and enable the commenting infrastructure, but the comments eventually (on a timescale of hours) get rendered into static HTML in my git repository for long-term archiving, SEO, searchability, faster page loads, etc?

That sounds interesting.

My next question is: Does Disqus's API let me do this via... Disqus? Surfing through the API docs suggests that the answer may be "yes".