OK! This site (and more importantly, another site built with the software that builds this) is now backed up on the regular via git to the huge HD attached my Raspberry Pi. Good lord, that took way more effort than I thought it would. But I feel the relief!
If I want to go further, I can also push it to some other git location in The Cloud (though not GitHub because of size limits). Or just tar it all up and upload it somewhere on the regular.