Except, now my dashboards are gone. Turns out, Kibana creates its own index, named kibana-int for storing the dashboards and stuff. Oops.
Did I have a backup of my indices? No - it's just log messages, and the originals are still on their respective systems. We use ELK as a convenience when things are amiss, which rarely happens (except when I go around "cleaning" things!). So I had to spend an hour rebuilding my dashboards. The new one is actually better than the old one, so I suppose that's the optimistic view of the story.
Here's the tip: Export your dashboards to a local file, and keep them under source control, like git.
Then, if you ever need to reload your dashboard after a disaster (or a "cleaning"), you can just load it from a local file in the Open Dashboard menu. Bonus: You can also open a dashboard from a Gist using the same Advanced screen under the Open icon.