The only marina on the lower Mississippi River from where you will enter it off the Arkansas River is at Greenville, Mississippi.
I have made the trip from Little Rock to the gulf 3 times. The person I know that has made the most trips on that part of the Mississippi river is my friend and your surveyor John Linck. If your conversations never got around to the trip, you should call him and ask about anchorages, etc.
Should you need fuel after Greenville, in the past the Vidalia Dock and storage in Vidalia,La would call in a fuel truck and if space available allow you to tie off to their docks overnight. They are a commercial business but will help the occasional non-commercial boater. They are on the La. side of the river across from Natchez,Ms.
Gary