@berkeman :
I think that while going in a zigzag path, the frictional force acting on the tyres will be reduced. Suppose that the inclined plane makes an angle A with the horizontal, friction coefficient is u, and the cyclist is driving on a zigzag path. Consider a part of the zigzag path - if that part of the path is inclined at an angle (say B) to any line parallel to the inclined plane surface, the maximum frictional force will be u*((mgcosA)cosB). If the cyclist rode on a straight path, the maximum frictional force will be u*(mgcosA).
Thus, it will be easier for the cyclist to go uphill in a zigzag manner.
There is a temple in my native place, and to reach that temple you have to climb 300 steps from the ground. I once noticed a priest, almost 30-40 years elder me, walk uphill much easily. He was walking in a zigzag path, which for once seemed weird.