When a freezer is under "real" conditions, like 0 degrees or lower, the stratification is not an issue (although it occurs) because the food is frozen. To keep our beers all the same temp, a fan is required.
Just get a computer fan, wire it to an old cell phone charger, and put it in the keezer. screw it to the top with a couple of spacers for air, or glue a magnet or two to the edge and stick it to the freezer wall. That way it's always on, not just with the compressor - Otherwise, the keezer only turns on when the probe's 'layer' is warm enough to activate.