It appears the 531 amps RC you mention for the AGM-31 are listed as only 300 using the normally referenced 20 hour rate. I don't know how much power the inverter uses just by itself, but the 156 watt
fridge will be drawing as much as 13 amps at 12 volts when running. Do you have enough
solar power to recharge the batteries at that rate, or are you just looking for something to cover you for a couple of days between hookups? (I am not an electric expert so my numbers may be way off)