There is a route, called the Great River Road. Well, I think there's a guy with a somewhat-similarly-named blog who might just have to ride it.
Based on a cursory investigation, it looks like the Great River Road starts at the Mississippi river headwaters, and follows the river all the way south. That's 3000 miles of Big Muddy awesomeness, is what that is. I may be sheltered, but this is the first I have heard of such a thing. I mean, I assumed it was more or less possible to follow the river south, but I didn't know someone had conveniently laid out a route for me already.
It's going to have to be done.
...After having a glance at a calendar, it's going to have to be done next year, probably. Dang it. On the other hand, I can probably explore a bit of the road close to home before the end of the riding season. Hmm.
Details here: Great River Road