Unless you have a jet pack on the Morgan
(in your signature), it's pretty much a no go.
The Tombigbee will have currents in sections but those will usually be manageable and there marinas
closely spaced, so you can rest and get fel. Unless the flooding is really bad...difficult but doable.
will be your problem. Currents are slower on the insides of bends and near the shore but no counter currents of signifcance. Also the commercial
traffic decides where you get to go when you meet. More importantly, the Mississippi is loaded with wing dams that will happily take out your keel
if you hang out near the edge. In the spring you can expect 4-6kts for long stretches (not the half mile under the blue water
bridge you reference). It's unsafe to travel at night due to debris (worse in the spring) and there are no fuel
docks till you get just south of St. Louis.
Even in the summer/fall when the current ebbs it's still mostly above a 3kt current.
We've gone down twice. To give you an idea I set the throttle at around 1/4 (4-5kts) and were averaging 11kts.
People don't go up for a reason.
Now if the new boat has a 300mile range at 25kts, it is doable.