Hi Gene,
There is no question that the Iota does a good job on shore power.
The real question is it possible to "fool" the ECM module into sending the necessary energy to the house battery and subsequently to the inverter. The ECM "sees" the starter battery. If it is fully charged then the ECM throttles back on the charging rate.
I have seen up to 70 amps flowing to the house batteries when I was experimenting with running the roof air from the inverter. That was great--but I was drawing 176 amps from the battery bank.
My system with twin #8 charging paths does not quite keep the house bank fully charged when running the fridge via the inverter.