Vibration in water pipes

I have a unique situation where my hot water heater is fed by city
water @ 60psi, and my cold water comes from a well at 30-45psi. I have
a pressure compensating shower valve, it is designed so that if the
water pressure on one side drops, like someone flushes a toilet, it
compensates for this so that the water temperature coming out stays
the same.

When I use it, and have it set to mix hot and cold at certain
temperatures, I get a vibration in the pipes, and the water coming out
of the shower head pulsates at about 4Hz or so. My guess is this
pressure compensating shower valve cannot properly adjust to the
extremes in water pressure difference, and/or isn't properly dampened,
and so it oscillates instead of stably regulating the temperature.

Replacing it is easy - after I tear out the walls. Don't really want
to tear out the walls. Anyone have any suggestions as to what can be
done about this short of just replacing the shower valve (assuming it
is the valve causing the problem).