I think the best solution to these problems is to split the AC bus
With the heavy loads feed directly via shore power/gen set
These would be the HW tank, battery charger, ice maker etc
And the 'light loads' supplied via the inverter such as micro wave, ac outlets #1, ac outlets #2 etc.
The advantages of this is
Inverter will never power the heavy loads
Impossible for inverter and Battery charger to be on at same time
Note: when plugged in to shore power/gen set the inverter acts as a simple pass through for the light loads (the actual inverter is out of the picture)
Other cautions when ruining inverter:
All Ac breakers off initially, turn on loads one at a time
Disconnect shore power if for some reason you want to invert or stated another way be sure inverter is off when connecting to shore power. Yes there is voltage sending in the inverter, that's not full proof as we found New Year's Eve a few years ago
Consider an AC ammeter to knyow what your ac loads are
Be aware of the efficiency of the inverter itself the quoted number of 80% is what I thought it would be
Real life experience on the Pro Mariner 2500 shows its worse based on actual ac and dx current measurement
Once I remember how to do it I will post a simplified AC Disgram showing how to split the bus.