What is the wiring diagram of the ZDE? I couldn't find any wiring schematic, the only pictures I can find are of a PCB with a blob and the "plug in" wire look like they're paired up (two wires for each switch). This leads me to think that it's possible that the switches don't use a true ground as a reference for the switches like the Naomi board does. For example, I've come across some controllers that supply 1/2 voltage on a common rail so analog sensors can detect a +5 or a 0v condition. This allows one pin to sense two switches at the cost of ghosting.
You also might have a short somewhere in your wiring. I think you said both boards are segregated through the switch. But how can the be if removing the Naomi board fixes your problem?