With the truck system holding truck battery voltage at 12.2 while the inverter is running, I suppose the truck battery could be losing some AH? I have no idea what the current out would be at that "loaded voltage" It is a starting battery so it can't take much.
Or is the battery still not being drawn down, but it is just showing that loaded voltage and the voltage will bounce right back? It would not take long to recharge the starting battery after the TC charging session has been completed of course. Just leave the truck on a bit longer.
Would it help to stop the TC recharge every 20 minutes and let the truck battery get recharged for a few minutes, then go back at it? That way the truck battery would be doing shallower cycles sort of?