One more thing to consider is if you're feeding the on board charger DC, you're putting all the current (albeit constant, not half-sine pulsed) through 1 pair of diodes when normally both pairs would split the load. This may cause heating/reliability issues long term if it wasn't designed with enough margin. I couldn't find a proper schematic for the charger to figure this out but there was a generic block diagram from a test report some university/group did on the charger efficiency which showed it was a standard switching PSU design followed by boost converter up to battery voltage.
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