Nick,
Assuming that the boy dose not let go of the rock but moves the rock along the centre line of the boat in an arc, then theoretically the boat will accelerate forward while the rock is accelerating in its arc and then decelerate to a stop as the rock decelerates, but overall moving forward and stopping and not oscilating
I do not feel the system is elloborate as it lends it's self to constant speed power mechanical sourse, driving through ofset gears. An electric motor or servo per reaction weight performes well and also has excelent controllability.
Best Regards
Jiff