I've been working up to this for a while, and when it came time to finally do it, it took about 20 minutes, and most of that was spent thinking about how to do it.
There's a new nodetype, river. It has one required attribute, url, which points to the JSON file containing the river data. The JSON for my personal river is here.
You can find yours by doing a view-source on your static river.
You might have to stare at it for a minute to figure out what it is.
There is some CSS collision, the CSS for the river defines styles for a navMenu. Ooops, that happens to be what we call the menu in the World Outline. That suggests we're going to have to come up with an abbreviated CSS for rivers.
Also, I'd like to see the river flush with the left edge, and indented by <%leftIndent%> pixels.