Hey John & Jane.....that new refer looks nice. Is that finish brushed platinum or ??
Power wise, I think you'll find it typically runs a lot less than 500 watts.
This guideline for solar apps estimates 380 watts and 1450kwh for a year (about 165 watt/hr average):
http://www.oksolar.com/technical/consumption.html
On my solar system here at home, I have a digital energy monitoring that charts both my usage and the solar generation to my laptop. So on a real time basis, I can turn my refrigerator on and off and see the change in wattage. My 2004 Kitchen Aid only pulls 160 watts, but since it is 26 cubic feet, I think the duty cycle is longer than yours will be.
Regarding running off the inverter, one thing you could do is set the temp colder before you unplug from the grid. Then you'll have a lot of thermal momentum that might last half a day ..... depending on the extent of the heat wave you're in.
For boondocking, if your "Jeeping hobby" leads you in that direction, you can get your self a small generator. I have a little 650 Honda generator that runs 6-8 hrs/day on less that 1 gal of gas to keep my batteries charged (four 6v Trojan golf cart @120ah each). In your case you'd just run the refer during the day directly off 117vac for greater efficiency.
Let us know what power and duty cycle your new baby actually consumes.
Also tell Jane, I really like her t-shirt too!
Good luck,
Bill