Why does a wound-rotor induction motor produce a higher starting torque?
With a wound rotor motor, increasing the rotor resistance doesn't change the maximum torque, but it causes the slip to increase reducing the speed at which the peak torque occurs. At a certain added resistance, the peak torque is reduced to zero speed.

Counter emf is not generally not used in induction motor modeling and analysis. The mechanism by which electrical energy is converted to mechanical energy is modeled by a variable resistance in series with the rotor resistance.