I do not have a basecamp or
12 volt fridge. But...if I did I would add a DC to DC converter to make better battery charging and to run the fridge while driving. Maybe a 10 amp DC to DC converter.
I think the answer to your question depends a lot on the TV. Some tv charging sysems will provide some battery charging while driving, others not so much. My Dodge diesel puts almost no appreciable charge to the trailer batteries while driving. However whatever drain is on the TV battery will be refilled by the alternator while in transient.
If I boondocked even a little with a DC fridge I would think about a lithium battery conversion and carry a solar panel or a small generator. Actually I see you already have the solar panel. The lithium battery will double your run time over a AGM and will recharge much faster with the solar or while driving.