I would bite the bullet and get a propane/electric powered refrigerator! The amount of propane the fridge in my trailer consumes is minimal so I can run a very long time on a tank of propane! The propane/electric refrigerators are just to convenient and do to good of a job to cobble up a solar/battery/invertor solution.
I don't know the ins and outs of the RV fridge market but there has to be many choices available. I can't imagine you won't be able to find one sized right to fill the hole your current reefer occupies. Propane refrigerators do require an external vent... I am guessing your trailer already has the appropriate vent. If it doesn't then... hmmm...