I can neither confirm nor deny that it was intentional. But, the Mississippi and Missouri have both been called the Big Muddy.
For my math, I used wiki “lower Mississippi river”, mostly. Forget what value I had used for St Louis. But call it 100 or 160 meters above sea level at St. Louis to 0 in New Orleans, 1600 km distance between those cities. 160 makes the math easy. That’s a drop of 1m for every 10km.
In Physics classes, you are usually looking at equilibrium or steady states. If bouncing a ball off a wall you use velocity before impact, and the velocity after the ball is coming back. You don’t look too closely at what happens during the impact. (Pet peeve, cause I can’t even guesstimate how long the ball and wall touch). For water flow, looking at average heights away from where ocean & river meet is easy. Understanding what happens where two heights of water meet, or fresh and salt, or effect of big rocks in the water is complicated.
I’m not sure if this is an example of “simulation is hard”, or “corps of engineers didn’t plan for this”. During one of the big floods, there was a flood barrier closed to protect the city downstream. Unfortunately, there was a stream entering the Mississippi just in front of the flood gate, and the river was so high that river water hit the gate and overflowed/was deflected up the stream. We sandbagged a neighborhood that did not know it was a flood risk. And wasn’t a flood risk unless the flood gate was closed. There was so much water that I think it had to come from river water going up-creek. The creek source didn’t pump out enough water for a big flood that quickly, even if the creek end had been walled off.
So, define “flow reversed”. From a big picture, you still have high water upriver, low water at the mouth, and a flow rate that can’t empty the river fast enough. At the zoomed in, messy level, you would have to consider ocean being higher or having some sort of “pressure “ analog that would push it into the river, and how, where and how much mixing of river and ocean water, if the river current pushes a current of flesh water a little bit into the ocean, etc etc. My feeling is the difference between low & high tide can push salt water a small distance into the river.
To get actual answers, I would use some probe that can measure salinity at different spots under different tide/flood/flow conditions. Also, finding where fresh water plants give way to salt tolerant plants - to first order that is how far the ocean forces itself into the river.