From what I have researched, a prop has two different speeds where the propulsion efficiency is zero. The first and obvious one is zero speed. (hover and ground run up), the second and much less obvious one is the plane's speed is high enough for the prop to have zero slip. In that situation, the prop blade's airfoils have zero angle of attack to the airstream and so are making zero lift. At a zero lift angle of attack, an airfoil's lift to drag ratio is zero.
Maximum efficiency tends to occur when the advance ratio is around 80% of the pitch speed. (20% slip) At lower slips, the efficiency actually drops off because the skin friction and form drag of the blades still requires power to overcome.

Yes, often the best performance does not come with the most efficient prop but with a tradeoff between prop efficiency and the ability of the engine to make power. With electrics, the efficiency of the system is the prop efficiency X the motor's efficiency X the gear reduction efficiency. Don't obsess on one and overlook the other two.