^ The 120W was for the battery circuit outlets in the trucks. Yes, the inrush current can be quite high and perhaps more than 10A for a very short blip, but typically the fuses in the truck won't react that fast, I would think. The 10A is standard for power outlets in trucks and it's starting fridges just fine normally if the voltage is high enough. So that should not be a problem with a battery unless the wiring is too skimpy.
I don't know yet what the issue is with the power supplies, though, it is possible that they were not capable of delivering enough instant power for the inrush surge. I may try it on a 200A supply I have and see what happens, but that one surely has a crappy waveform.