If an experiment shows that there is no difference, what is the explanation?
The experiment is flawed. If you can stop the prop whilst maintaining the attitude for best glide (e.g. by feathering), there is a benefit in doing so. In practice, however, in an aircraft with a prop that cannot be feathered, any benefit in gliding range from a stationary prop is more than outweighed by the height lost in stopping it aerodynamically.
Bulldog props used to stop in the spin all the time. If it didn't re-start itself in the recovery, a quick burst of starter always did the trick.