[Renoir]

Mast pumping IS caused by harmonic standing waves. The only question is how to provide an attachment which will alter the harmonic to a value which will not be sustained by existing geometry.

Because your inner stay stops the standing waves I will bet that the attachment geometry is altering your 1/4 or 1/2 wave vibrations. If the runners are directly opposite the inner stay attachment at the aft side of the mast section (or very close to it) they also alone should stop the vibration if they are set up with a sufficiently low modulus of elasticity and a high enough tension. Note mentally that the runners form two vectors which you can use to calculate literally just how much tension each one must have in order to equal the total tension put on the mast by the inner stay when is is attached an successful at stopping the vibration. Play with that.