John,

Without knowing what type of refrigerator this is hard to answer. But my thought would be that enough Solar to run the fridge would entail significant expenditure. Better solution might be enough solar to maintain the batteries so that the inverter could handle the startup current for the refrigerator compressor. Then enough solar to keep the batteries peaked.

Regardless, you need a solar charge controller that will regulate the current being supplied to the battery bank to ensure you don't over charge them. 

John,

Others may chime in, but I've looked at similar options for our 39F Discovery, and the cabling up to the existing solar panel is far too small a gauge to handle major panels. That said, the rear cap offers an easy way to get the heaver wiring down to the batteries. Rather than trying to rewire the existing items, a charge controller for the solar panels will regulate the charge into your 6v batteries keeping them always peaked when possible. Since the solar charge controller is such a minimal part of the cost to go solar, to me it is the easiest and most reliable path to take. When I do it, I also plan on upgrading the batteries to have greater storage capacity allowing for much longer run time. 

Basically the solar panels are the battery charger for when you are boon docking. This allows the batteries to handle the heavy startup load without having to size your panels for that high draw. Most residential refrigerators have such good insulation that they hold their temp for long periods without running the compressor.

A quick google will show you choices for controllers from $12 to $3000. A 60 amp can be purchased for under $200 while 100 amp units from folks like Magnum will run up about $900.