Quadcopter propeller performance
When testing the propellers for these quadcopters, would it be useful
  to test both the right handed and left handed rotation of the
  propellers or just one direction?


You may miss something about propellers rotation. A given propeller produces thrust (which is another name for lift) when rotation occurs in the designed direction. When direction is reversed, thrust may be produced, but not efficiently, and will be reversed compared to the regular lift.

A propeller is a wing in rotation. Wings are not used is reverse direction, with a plane going backwards.

Left-handed and right-handed propellers are different:



Thrust is determined in the intended direction of use.


  Why would a designer select a lower pitch to diameter ratio


For the same reason than wings on actual planes have an optimized size and incidence. Increasing this size or this incidence is not productive. The limit may come from different reasons, but essentially for weight and drag considerations.

In the quadcopters, the propellers are spun by electric motors that have a limited power and a preferred rotation speed. Propellers are selected to match the rotation speed and available torque of the motor.

In addition turbulence is created by the propeller, especially at high pitch. Turbulence can decrease efficiency of neighboring propellers, so a compromise has to be found between high individual and low overall lift produced.


From Studying the Aerodynamics of Multi-Rotor Drones (Nasa)

Also think about the fact that a propeller just converts a quantity of work (rotation) into another quantity of work (translation of air). The rate of conversion is dependent on the blade pitch. Air translation (lift) can be increased but not beyond the capabilities of the motor to create the equivalent rotation. If this is done, the motor just can't deliver, and it's efficiency decreases (battery will be empty more quickly).