@Joey Hess my experience has been that selecting appropriate transducers, siting them correctly and mounting them well is half the battle with automation.
In refrigeration, stable systems are designed by appropriately sizing the components, and running them at pressures and with valving to achieve the required temperatures. Lotsa folk don't understand this: they tend to think that if you want colder, you just put in a bigger compressor etc.
You have an interesting challenge here, as the refrigeration in your unit is specifically designed to freeze: the evaporator part of the setup is pressure fed and jetted specifically to yield temperatures below 0'C
What that means is that the controls must intervene more agressively than in a refrigerator, which will be optimised to run over 0'C
(Okay, that's theory, certainly applies with industrial refrig, where we sometimes have to 'de-tune' repurposed cold spaces. I don't know to what degree it applies to domestic setups, but it will be a factor.)
One way to look at this might be as follows:
The air in the box has a minute thermal mass when compared with the steelwork.
So we can expect the air to follow the temp of the steelwork, provided the two are in contact.
So maybe identify what parts of the wall and floor are cooled by the refrig system (perhaps the upper walls, but I don't know), bond a temp sensor to the steelwork there, and control off that.