It sounds like your stack fan is being used to cool the volume behind the
fridge and not just the stack. That sounds good and the temp range of the switch sounds good too. One of the best ways to make
propane fridges work better is to install a fan to assist the natural draft of the compartment behind the
fridge and keep it cooler.
Putting fans inside the box can help equalize the temperature of the food inside, especially if the box is relatively full, because the system no longer relies on natural convection.
But it can also make temperature control harder depending on where the sensor is. And it can freeze the food instead of just cooling it. The whole box tends to go down to the temperature of the cooling fins of the evaporator, if the temp sensor is on the evaporator.
The box might cool faster, but it cannot cool faster than the capacity of the cooling system, the fan just delivers the box heat to the evaporator more efficiently, but the evaporator can only remove so much heat from the box.
I installed a fan in my boat
refrigerator, which was a top loader with a lot of insulation. I was able to adjust the box temp right down to 32 degrees. Everything in the box was that temp. Just barely above freezing. Food lasted much longer that way.
In the trailer, it will also mean the system runs more. This may not matter with
propane, and colder means the food will last longer, but with a compressor
fridge, running more means more power is used. With the compressor fridge in my Xplore, turning it down freezes everything in the chiller section, and pulls the freezer section down to about 5-10 degrees below zero. It can go from running about 10 minutes per hour at normal settings to running continuously when turned way down. In that fridge there doesn't seem to be much need for a fan in the box.
I just discovered that my side-by-side home fridge was not cooling the main section much and was getting up to about 55 degrees. That fridge uses a continuous running fan that transfers cold air between the freezer and chiller sections. The chiller temp is regulated by a set of louvers that are motor controlled and were not opening. So I stuck various things in the louvers to hold them open different amounts and watched the fridge temps, looking for a fix that did not required replacing the temp controller.