For overall dough consistency, we don't recommend allowing the dough to ferment at room temperature before putting it into the fridge. The change in dough density makes the dough too difficult to cool uniformly. Instead, immediately after mixing, take the dough to the bench (counter top) cut and form the dough into balls, wipe them lightly with oil and place into individual plastic bags (bread bags work well), DO SEAL, but instead, twist the open end into a pony tail, and tuck the pony tail under the dough ball as you place it into the fridge. By doing this you don't need to use a dough box, and there is no fear of the dough balls drying out. To use the dough, remove from the fridge and allow to temper AT room temperature for 1.5 to 2-hours, then turn the dough out of the bag into a bowl of dusting flour, then open into pizza skins using your perferred method. The purpose of cross stacking the dough boxes (applicable to pizzerias) is to allow for uniform coolong of the dough without the development of unwanted sweating due to condensation forming on the dough during the cooling process. The use of the plastic bags makes the need for dough boxes unnecessary, and it is more compatible with a home refrigerator with its space limitations.
Tom Lehmann/The Dough Doctor