Yep, looks clearly as if your Z axis suffers from heavy spiking. I'm afraid the only temporary solution is to disengage the Z-axis and using keyboard only for rudder control, until you get a new stick.
I had to do the same when the same axis on my (then 4years old) Saitek Cyborg started to spike excessively. However, as this is the only trouble with this stick, I still use it, having acquired pedals 1 1/2 years ago.