The biggest difference is the dough quality. If you are using a standard home mixer, like a KitchenAid stand mixer, you will not get the same quality dough that a pizza operator will get using a commercial mixer, like a Hobart mixer. Their dough balls will have a better developed gluten structure with better gas retention, handling and shaping characteristics. They also use commercial plastic dough boxes that are held in a commercial cooler that operates several degrees lower than your home refrigerator. Unlike a home refrigerator, where the door is typically opened several times a day, the cooler usually gets much less traffic, so the dough balls aren't subject to temperature swings. In fact, some pizza operators make their dough balls at night, usually at the end of the work day, so that the coolers get almost no traffic until the next day.
You might think that you are using less yeast than professionals based on what you have observed, but if you are using a basic Lehmann NY style dough formulation, that formulation is one that was developed for pizza operators, not home hobbyists. Of course, it is still possible that pizza operators are using more yeast (it could be even less) than you are, but that doesn't diminish the value of the dough formulation you are using.
I suspect that the pizza operators don't have the sticking problem you have because of the plastic dough boxes they use. Usually, they use dough scrapers to lift the dough balls out of the dough boxes, or a special tool that is designed for the same purpose. In your case, if the dough balls are sticking to the bottom of your containers, the obvious solution is to oil the containers before placing the dough ball into them. Or oil the entire dough balls before placing them into their containers.