RS 485 ground signal and chassis
Looks like a common mode voltage problem to me. Although differential signalling, it still needs a common GND.


(source)

Replace your 1nf 500v capacitor with a jumper. Or wire signal ground to all nodes.
Shield still stays connected to earth.




  The shield is connected to the Chassis ground on the various devices in the loop - and not at the 'master' end - no ground loops.


This could cause ground loop problems.


  Will connecting the zeners to chassis ground work, and save the data lines from dangerous voltages?


Typically, RS-485 tranceivers can be protected by an TVS diodes.
For CAN bus, the NUP2105 is popular. You connect this to the data line and signal ground. Not earth, the tranceiver is not connected to earth since they are galvanically isolated.

*earth, as in mains earth.

I found this RS-485 design document from TI that might be of interest.
(slla272c)