With great thanks to Ragbrian for his help routing through St. Louis and his assistance riding most of the distance, I've finally (after quite a long time) compiled the data into the complete route for Missouri.
Be aware of a couple of anomalies in the route. Part of the MRT follows a bike-only path through St. Louis. At one point in the route (if you're riding south) you'll approach a T intersection where the MRT clearly points left, but the route says to turn right. This is correct. On a motorcycle, you'll follow the road, rather than the MRT which turns into a bike path.
South of Cape Girardeau, there are some discrepancies between what the online maps say and the signs on the road, moreover, the signs on the road do not follow a logical route. So, I made my best guess. The route ends at the Hickman Ferry, which occasionally closes due to weather or water levels.