I believe the charger cycles, first bulk and then down as required by the batteries condition. The bank must be down a bit or charging would not be necessary. Even if you didn't double the chargers input with the gen, you still don't have enough.
I notice your AC panel shows no incoming voltage. Is this with everything turned off except the main double breaker? What kind of adapter are you using to go between the generator and the shorepower inlet?
Living aboard in Victoria Harbour