Andrew, you are getting some expert advice here, but you still might try what worked for me since I had the exact same symptoms as you describe now: random low-voltage error codes at the engine room modules, a an engine randomly going into forward at start up, sometimes with beeping.
The very knowledgeable tech manager at my Marina advised me that I would need new controllers and new modules because they were the 2006 version and obsolete. We got on the phone to ZF who nicely listen to the problem and agreed with him to replace, the controller, harness, and the modules, because they were obsolete. The boat was new to me, and this problem did not start occurring until a month after I owned it. The boat had sat for two years previous to my purchase.
Drawing upon my 1970s electronic tech training, I decided to give it one more shot for repair. Considering the low-voltage random alarms, I took a new pencil with a fresh eraser on it and carefully cleaned all of the little pins of the control cables connecting to the engine room modules. Do not bend the pins because you could cause a crack further up and never be able to figure it out. I did not see any obvious corrosion, but that fixed my low-voltage error.
Unlike you I had just one station. My throttle look a little different than yours, but I remove the entire unit from the helm and looking up inside from underneath I saw the throttles arm move a wiper across a series of contactors. Using my same high-tech pencil eraser, I gently cleaned each of these pads. I noticed possible filmy corrosion on the offending engine side at and near the neutral detante. This fixed the random start up problem.
I never had another problem with the ZF Mathers system. It was fantastic because with the buttons I could sync my engines, or switch into troll mode, or have high or low idle. And of course, I did not lose use of the boat, waiting for all the parts and people to come to put it together.
YMMV
Good luck taking care of your hole in the water.