How many cubes of food do you think can be held in those tubes that aren't being chilled? How many days do you think it will take for that stuff to rot?
The correct way to do this is to have a closed loop of water running through the fridge that the dosers (inside the fridge as well) are tapped into. As the chilled food is pushed into that closed lupe via a peristaltic pump, it will rush the food to the display. Otherwise its gonna rot in a hot second unless youre using such a short length of tubing that its no longer practical.
The way I am going to try is reverse the motor for a period of time to have air bubble stir the chilled food inside the cooler. Then forward the motor to dose food, then reverse again to purge food out of the feeding tube. This is just an idea, like you said food might rot in tube. Shorting the feeding tube will help but still need flush from time to time.
Don't have room for a mini fridge. I saw someone using a wine chiller, but not sure how long it can keep food from rotting.