This contest sort of looks like a maze. Except the track is more like a road, but still you have a lane where the robot has to be at all times. In a maze, the robots will follow one wall, left or right, depending on which one leads to the exit faster. In more advanced mazes, such thing is not possible, so they use a combination of methods.
So, I am saying that you could follow the left or right line and use a PID control to keep the robot's movement smooth. This way the robot will not be confused when both sensors are over the line. In each corner of the robot, install 3 sensors for line following, a bit out from the robot, so only if all sensors are past the line the robot actually starts crossing the line. This way you can decide at the contest which line you're going to follow. Those 3 sensors can be installed at an angle, so they kind of look like an arrow ( / \ ), use the outer sensor to follow the line and the top sensor to detect sharp corners.