I've used the same logger at work and seen similar graphs.
Keep in mind that the controller will only get you so far. The up swings in temperature are based on the insulation and the thermal thermal mass inside. The down swings are the cooling cycle. Your graph will look different depending on where your controller probe is located and where the logger is located. I'm assuming you're using an EasyLogUSB from ThermoWorks or directly from Lascar. These will only monitor air temperature in you freezer/fridge, so likely even with the controller probe attached to thermal mass, the spikes on your logger graph will be just as sharp unless you have some airflow.
Using a programmable controller will get you narrower swings, i.e. lower highs, and higher lows, but you have to compromise that with shorter and more frequent cooling cycles which may shorten the life of the compressor.
Placing the probe in a bottle of water, or attaching it to something with more thermal mass will cause less frequent and longer cooling cycles, but it may
show up on your graph as wider swings since your logger is monitoring air temperature.
In my opinion, if you're really pinching pennies, why are you worried about temperature swings rather than efficiency? I estimated that I saved money by installing a controller on my mini fridge, because it actually runs less than stated on the tag on the back. I think the tag said average run time was 25% at a certain ambient temp, and with the controller I was getting something like 16% run time. I can read the temperature digitally on the controller, so I don't mind what the temperature swings are.
