Are you sure your Hercules 20 is an inverter?
I had one in my Jurgens XT140 but it was only a charger.
Solar panels on the roof are only good if you never park in the shade. Also you cannot angle the panels to follow the sun throughout the day.
Deep cycle batteries are necessary because the discharge does not damage the batteries very much. Running your fridge for 24 hours will discharge a car battery to the point of damage (if there is no sun to recharge).
Why do you need an inverter? Hopefully not for extended use. The efficiency is low and will drain your batteries quickly.