Yellowstone would be a thousand times worse than any conceivable New Madrid event. Yellowstone not only has direct effects with huge amounts of ash ( twenty to a hundred foot deep in places with some 1-2 inch estimated ash falling as far away as where I live in NC) but it will have a worldwide climate effects immediately. We are currently between glaciations of the Wisconsin ice age which will eventually return on it's own but a supervolcano or large enough asteroid/comet impact can throw the switch and within a year we would be well into the next glaciation event ( an ice age).Yellowstone is a powder keg that could blow any time I'm sure. Not sure if it would be worse than another major shake up of the New Madrid Zone or not but it would be bad for sure.
The parts of the river that were going backwards were from subduction of large areas of land re routeing the river itself. That also created Reelfoot lake.