In a worst case situation I would also worry about the lack of cover on the water. Perhaps traveling at night but that would make the navigation harder. There would be the noise from a motor boat that may attract unwanted attention.
Yep, that's the biggest danger in the scenario I've drawn, because a river only goes one way and you have to follow the river. Any potential stalker knows where you will be in the future, and so can set up a perfect ambush. The smaller the river, the worse the danger from onshore, because not only is he more likely to hit you, but he feels more confident of recovering your gear and so has a stronger incentive to attack.
On a big river like the Mississippi you can get some protection from an ambush by staying near the middle, but then that exposes you more to pirates who have bigger boats, more people and bigger guns than your party.