How to further dampen vibration cascading on piezo-elements?
That relation could perhaps be solved if I would have less sensitive
  piezo-elements. Do those exist?


This is usually solved by putting a resistor across the piezo element. You could start at (say) 1 Mohm and reduce the resistor value in steps until you get the desired sensitivity. 

You might also find that if the piezo is hit too hard you could damage the arduino inputs so "dampening" is recommended plus adding a series resistor between arduino input and piezo element (maybe 10 kohm). If you could describe the interface better more help could be given.