I had a similar problem on my Seeburg E.  The spill valve would
oscillate on play, when there were no demands on the suction, and
on rewind.  The valve flap was exhibiting an un-damped self-excited
oscillation, so the solution was to add damping.

I built up the opening end of the flap with a small block of wood,
about 1/2" high, to give a smooth surface at right angles to the
moving board of the reservoir.  I then made a thin flat spring out
of shim steel, screwed it to the moving board so as to press lightly
against the new block.  The spring pressure of this damping spring
must be insufficient to stop the main flap spring from closing the
flap.  The damping provided by this new spring stopped all vibrations.

There would be other ways of stopping such a vibration, such as
changing the size of the spill aperture, but this would require more
intervention in a restored instrument.

Nicholas Simons, GB