While proofing, the crust can appear on the dough balls if in contact with air (oxygen). I tried preventing by damp cloth but it still happens. The only thing that works 100% is plastic foil wrap, but that would prevent the dough from rising. I'd like to proof for long time this time, so it is even more important to get that technique right.
If you insist on using a damp cloth, you have to make it wet again and again, so this is quite cumbersome especially with long proofing times.
Much easier is plastic wrap, which doesn't prevent the dough from rising if you use it to cover a sufficiently large bowl. Tightly wrapping the dough itself obviously won't work.
My prefered method for these very long raises is a large food-safe plastic container with a lid. It doesn't have to be super-airtight and as I usually do a round of "stretch and fold" or quick punchdown every 12-24 hours I never had a problem with dried or overflowing dough.
Try coating the dough ball with a little olive oil or a non-stick spray. I don't know if that's the reason why but it's what I always do when baking bread and I never have a crust form during the rise.
Commercial pizza places usually use plastic dough proofing trays. They interlock and provide a relatively air-tight seal when they stack on top of each other.
If you're looking for something that fits in your refrigerator, you should look into Artisan DoughMate trays. They are are 1/2 of the size of standard restaurant sized trays and you can fit a couple in your home fridge (Just under 18" x 14") They stack with a very good air-tight seal and you just need a lid for the top one.
You should be able to fit about six dough balls to a tray.
If your only talking 2-3 dough balls then one tray would work, with a lid. But you also can look at aluminum dough pans. Some of these are also stackable with lids, and you put one dough ball into each one.
I've often seen people spray the pans with oil so that the dough releases easily, or spray the dough balls so that if they spread into each other while proofing that don't make one massive dough ball.