Hate me if you want, but try using a bread bag or "food" bag (not a Zip-Lok bag). Just lightly oil the dough ball, drop it into the bag, twist the open end into a pony tail and tuck it under the dough ball as you place it in the fridge, if you want to stack them in your fridge to save space, put the bagged dough in your existing plastic container uncovered for a couple hours, then cover and stack. To use the dough just invert the bag to turn the dough out. I like to turn the dough out into a bowl of dusting flour that I will use to open the dough balls into pizza skins. The dough maintains a nice round shape and doesn't get damaged or stretched during removal from the bag. You can reuse the bags a number of times too.
Tom Lehmann/The Dough Doctor