At this point I need a better battery and also use a low draw inverter. Yesterday was cloudy all day and things still went well. Researching old Embraco compressors they r very efficent and energy conservative. Don't know if these results apply to a modern compressor dorm fridge.
I am going to say this is totally doable at this time.
You need a decent battery, 2 Trojans if you want to run something besides the fridge and a LED light and a mechanical electric timer. Otherwise for fridge only I think a good 12 volt marine. Plus a panel capable of recharging a battery in one day. I would be very comfortable with my 245 watt 24 volt and my Eco Worthy MPPT conttoller doing all my electric needs with 2 Trojans. Otherwise probably for fridge only a 140 watt 12 volt panel with PWM controller and 12 volt battery. This Embraco compressor is awesome! More experimenting when I can fin a decent low cost 12 volt marine. I am not willing to use my Trojans yet. Besides there are 4 of them. I did notice last year in Quartzsite a lot of new travel trailers and motorhome come with electric fridges that are 110 volt. Some of my friends boondocking with 500 to 600 watts on the roof and run a inverter for full size freezer fridge units. Using propane seems out of style. Who knows...