So I've been thinking about this project far to much lately. I'd like to say it was mostly while drinking coffee sitting on the porch petting the dogs, but there was a decent amount of time spent online researching Phase Change Materials and insulation. I found a company that produces PCM in a variety of target temperatures who is willing to send samples, but they include a surcharge of $250 for the process of making anything under a ton. Hrmmm.
@Joey Hess, have you ran the freezer overnight as a fridge and looked at what the battery usage would be? If the unit only uses 600 watts a day as a freezer, it may only take say 150 watts of battery power to maintain temps at fridge levels at night.
As you've mentioned, using it as a freezer might be most effective as a "thermal battery" if you actually freeze some water and use the frozen material to cool an insulated cabinet or your other fridge. You could use insulated hvac ducting or insulated copper pipe to transfer cold air or a transfer fluid between the two. During the winter when there isn't much sun and it's snowing you could use your cold outside air as a cold source.