PROGRESS!!! 2/3, but still better
Thanks guys for the help - finally some progress that points towards a cause !!!
I replaced both PSUs (feeding the 12v/GND for the Charger AND 12v/GND to the Contactors controller) with a single car battery, feed through a switch and a 15A fuse. This allows 2 out of 3 modules to charge (any two modules concurrently charging, but not three). So the charger must be doing some kind of check (current leakage? power availability?) that if not passed prevents the requested charging from initiating. As additional modules are requested either the sensitivity of the test is increased or more likely whatever 'error' the charger is testing for passes a threshold. It could be that swapping from PSU to Car Battery made the difference or just messing with the cables and connections was sufficient.
The odd need for a ground connection between the charger/HVJB cases (grounded to the EVSE) and the GND from the car battery is still necessary for the Gen2V3 card to be able to tell if the EVSE button is pressed, connected, or unconnected. When that ground is missing - the Gen2V3 card oscillates from Pressed to Connected. I suspect that the GND connection from the EVSE is connected to the Model S grounds just after the charge port. So while this looks like an odd ground connection in my setup, it is normal for the Model S (EVSE ground connects to car's body ground rather than to the HVJB case).
Also, I have a laptop with USB connections to the Gen2V3 charger card, and also to my Battery Contactors controller. The 2/3 charging symptom occurred whether or not the laptop was also plugged into 120v power (i.e. battery vs wall plug).
So some things to follow up on next...
1. Further cleaning up / increasing cable size on the 12v lines.