Why stirring the cyclic helps in stuck left pedal?
The R22 has an anti-clockwise rotor. The more torque the rotor exerts, the higher the clockwise torque on the helicopter will be: nose right. With a stuck left pedal the nose wants to turn left, so we want the rotor to exert more torque.

On pumping the collective: there is an effect of how fast the collective pitch is raised, on the torque exerted. The figure below shows $C_T$ (a dimensionless measure of rotor torque) against time for a full sweep of the collective from full down to full up. Rapid deflection causes a torque overshoot, so a higher torque than a slow deflection.



So if the collective is raised fast and lowered more slowly, a net torque increase is generated while lowering the helicopter. Picture source: Helicopter Performance, Stability and Control by Raymond Prouty

On rotating the cyclic: cyclic pitch deflection causes angle-of-attack variation of the rotor blades, with an associated variation in blade drag, and therefore rotor torque. There is a section on this effect in the book Principles of Rotor Aerodynamics by J. Gordon Leishman (section 8.15.7 Unsteady Axial Force and Airfoil Drag). What I can distill from this chapter is that stirring the collective clockwise creates more airfoil drag, while keeping the net movements fwd/aft and left/right neutral. Unfortunately the section does not contain any helpful diagrams.