So let's assume a light piece of aircraft wreckage slowly sinks
What do you call a "light piece of aircraft"? The tail section which has been recovered is weighing at least several hundreds kilograms and probably more than a ton. Once this kind of piece has sunk (less than 30m deph) in the mud and due to the shape of this part (asperity), I doubt that it could have been dragged along the bottom even with a 6kts stream.