Bernt, this may work.  I have the same problem with a player accordion
regulator that I built.  Its construction sounds very similar to the
one you described.  Based on the speed of the turbine I can cause the
oscillation to happen on demand -- there seems to be a "sweet spot"
(if you can call it that).

Unfortunately it oscillates every time the turbine is started until it
gets up to speed, then it can occur during playing when more pressure
is required due to demand.

Here's a fix I have been told will work although I have not tried it.
I seem to remember reading in Craig Brougher's "Orchestrion Builder's
Manual" to glue a piece of plastic window screen (available at any
hardware store in small rolls) across the spill hole.  The spill
palette now rests on the screen and not just the bare open spill hole,
this should stop the oscillation problem.  Again, I have not tried this
yet.

Good Luck with the problem.  Please post if it works or doesn't.

Tim L'Amoureux