“My understanding is that the negative DC bus bar is connected to the chassis for grounding, and the inverter/charger is also grounded to the chassis. Maybe that common ground is causing an issue.”
No, the inverter AND the dc bussbar grounds both go to the common chassis ground... Something else is amiss...
If you’re empirically confident that the battery is up to snuff, and all the dc loads are easily accommodated via the battery (converter-charger OFF) when inverter is not in the loop, then I would begin to suspect (per Occum’s razor) the inverter...This assumes (??) that everything works just fine until you insert the inverter into the loop...JMWAG
