OK, let me give you some ideas. First let me remind you, no such thing as too much information. I'll assume your overland foray will involve overnight camping but not 5 days on one location. I looked up the 31M and here is what I found.
It is rated at 92 amp hours at the 10 hour rate. That means it can supply 9.2 amps for 10 hours.
In this case, your 50qt ARB fridge will draw around 2 amps, so technically it should run your fridge for about 45 hours. Now I said technically because the ambient temperature will affect how hard the fridge works thus altering the amperage draw. Also that is an average draw, it actually draws closer to 5 amps when trying to cool, which would bring the time down to about 18 hours.
So let's say you set up camp around 4 in the afternoon, you party that night and don't wake up until 8. Your fridge will have been running for 16 hours, and if the average amperage draw was in effect, you should be about 35% discharged. This should allow you to start your engine and start to bring your battery back to full charge.
But if you decided to stay camped you can now figure out how your solar panels will help. Assuming and actual 80 watts of output, we devide 80 by 12V and arrive at 6.6 amps. More than enough to operate your fridge, theoritecally. I caution that most of these things don't operate as advertised. But if yours gives you half the advertised capability you should still be OK. You can confirm the output with a decent DVOM.
Now let me remind you that the output of the solar goes to nothing without sunlight, and parking in the sun makes your fridge work harder. Also 35% discharge is alot, so you want to be aware of how low your battery gets if it is going to start your engine. In other words, get a voltmeter. Here is a link to a chart which indicates state of charge based on voltage.
Battery ?State Of Charge? Chart
So much more I can share here, but I prefer to answer your questions if you have any, as opposed to writing a book.
:der: