not possible - as there's only 1 input to the units, its on or off.
In the diagram in post 1 the battery & solar is connected together, the inverter doesnt know if its battery power or solar power its seeing.
I tried it yesterday, was getting ~1000W from the panel & had a full battery, so set the inverter to output 600W flat.
It was using the solar/charge controller only & didnt draw from the battery, once the sun went down - more & more came from the battery.
Yea mine does exactly that, I find as long as the solar is around 200~300w higher then the house load the battery is charging, less than that battery stays roughly same voltage until obviously less solar then house the battery discharges.
This is my battery voltage for yesterday.
What the solar looked like
You can see my fridge kicking in and out all day hence the ups and downs.