GSX doesn't control any of those editor keys directly. It will use whatever keys are assigned to the Slew events in the simulator. And, the Z key can be used only to change the height of the Parking System (VGDS or Marshaller). The GSX manual explains this at Page 38, by saying that Q/Z only work with the Parking system.
The picture at Page 42 shows the key assignment while editing jetways, and Q/Z change the logo here. Jetway height cannot be changed, you can only select a different model with a different height.
If all of this is clear to you, and you are only trying to lower a docking system, but the Z doesn't seem to work, than the only possible explanation is that some kind of another addon (maybe a camera utility) has already took that key, so GSX cannot use it.
Since these are standard Slew events, you cannot just reassign them, since you change the key in the simulator Controls option, if there's a conflict from another addon getting the same event, the conflict will still be there on the new key so, the only option is to find that addon and temporarily disable it while editing a parking in GSX.
