Woxman
The very description of the PIO manoeuvre gives the answer to the correct recovery.
A Pilot Induced Oscillation requires the pilot to do things with the controls in order for the PIO to start or continue. This the complete solution is to let go of the controls. If it was a PIO and you let go the aircraft will stop oscillating at once. And I do mean instantly become still.
If it was an oscillation that was fundamentally caused by the aircraft aerodynamics – for example a divergent short period oscillation in pitch on say a short coupled or tailless design - then letting go will not necessarily kill the motion. Clamping the controls might help but only with non powered systems. But be warned clamping is very difficult to do in practice as you will be thrown about by the motion and your whole upper body will be difficult to stabilise.
However I would ask you to rethink your notion of moving your hand down the stick. Gripping any stick lower down means you have to move your hand LESS for a given control deflection than when it is holding the top. This increases the sensitivity of the control system which makes you more prone to PIO.
If your thoughts of moving your hand down were prompted by trying to increase the force needed to deflect the controls then I am afraid experience suggests that any slight benefits from this will be swamped by the bad effects of increased sensitivity.
JF