Getting the mirror going was simple, because as I mentioned I alredy use Git for managing this site. Simply adding a new destination to publish to:
git add remote mirror <url>
and adding that destination to my deployment script was all I needed to do. Yay Git!
Thanks Manton for the awesome suggestion. It's important that we, as a community, try to persist our work. The web right now is ephemeral, so individuals need to take the steps make sure their work is preserved.