Using the scientific definition of work, does moving an object a greater amount of distance always require a greater amount of work? Why or why not?

The answer is no. If you are dealing with a conservative force and the object begins and ends at the same potential then the work is zero, regardless of the distance travelled. This can be shown using the work-energy theorem which states that the work done by a force is equal to the change in kinetic energy of the object.

W=KEf-KEi

An example of this would be a mass moving on a frictionless curved track under the force of gravity.

The work done by the force of gravity in moving the objects in both case A and B is the same (=0, since the object begins and ends with zero velocity) but the object travels a much greater distance in case B, even though the force is constant in both cases.