First, gently bent the freezer coils down using some heat applied to the tubing with a lighter (see scorch marks on tube). Also, removed thermostat by prying a plastic strip off the thermostat and removing a screw underneath. The black and white wire need to be shorted together for the compressor to turn on, so these are the inputs to your relay.
Ok, everything fits now.
Auber controller all wired up. Cut out the hole in the front of the fridge with a dremel. You need to be precise with this, because the face is maybe only 1/8 inch wider than the rest of the controller. Had to drill a small hole through the hump in the back of the fridge to run a wire that would carry one of the power wires for the controller, since you can use one of the black/white wires that were attached to the old thermostat as the other (see schematic on back of fridge). Also removed the door trays by unscrewing them from the door and pulling the rubber gasket off. Reattached gasket with the screws, hot glue, and waterproof caulk.
Controller parameters set. It's alive!