This was a bit hard to spot in the writeup, as I have no clue about how ice cream making and machines work. Otherwise we could just use ice, which will be as cold as the refrigerator can get it. (I doubt the endothermic reaction of dissolving the salt contributes very much to the cooling).
Now that I think about it, if I were doing this I would use antifreeze for the coolant instead of wasting salt. Bonus, I can store the antifreeze when done, but the salt water is wasted unless I'm going to use it to make some kind of soup or similar.