I went down the MS from Cairo to the cutoff into the Achafalaya a few years ago. It was an adventure. I actually enjoyed the trip immensely, but had some serious second thoughts the first couple of days, mixing it up with the big tows on the endless switchbacks north of Memphis.
Are there facilities on the Arkansas? When I went by the junction there was a big flow from the Arkansas. It looks like you've got a long way to go upriver after leaving the Mississippi. Not many pleasure boats around there...
The Corps of Engineers publishes observed and predicted water level for all the rivers. Be extra cautious if the levels are high or rising. A lot of debris ends up in the water when levels rise, and generally currents are higher.
Good luck!