Also, before I saw what the heat sink was, I wondered if you could use shotcrete on the walls of the freezer, to act as the thermal mass.
I think the chest style is best for total energy consumption. But as we saw, his biggest problem was around thermal stability. If we put the freezer/fridge fan under computer control, you might be able to get more stable fridge temperatures despite the air loss because you can drive the freezer temperature much lower, getting more stability value from the thermal mass. (And it's also worth filling in any big air spaces in the fridge with more thermal mass, so that opening the door is not a big deal.)
Depends how quickly you open it and slam it shut afterwards.