I have to contradict @saj14saj here. I have frequently had bread made with underdeveloped gluten (my grandma uses AP flour and tends to knead very short, 2-3 minutes per hand, and use very short proofing times). The bread is soft and cakelike, but it has no trouble rising, and it is neither flat nor dense.
On the other hand, I have had bread with exactly the same symptoms as yours - first feeling great, then left out for a long time to proof. After that, it looks good, but one touch makes it collapse into itself. The reason was very clear: overproofing. There is no doubt that underdeveloped gluten cannot have been a factor in my case. First, I am experienced enough to know when my gluten is developed - the bread was kneaded well beyond windowpane test. Second, it was a large batch of dough. I baked the first loaf at the optimal time and it rose just fine and had a nice texture with traceable gluten sheets through the crumb. It was the second loaf, which I baked a few hours later (and the proofing loaf spent them in a 30 degrees celsius kitchen in summer) which made the trouble. The dough had exactly the "loose" feel you describe, unlike the normal, springy feel before the proofing. It collapsed on touch and would not rise at all. It also had a very strong yeast fermentation taste, unlike the other loaf.
From your description and my experience, my conclusion is that overproofing until your starter died in its own waste products is the most likely culprit. The simple answer would be to not let it sit out overnight. The right amount of time to let it sit would depend on the room temperature, on the amount of starter you used, but also its leavening strength, and that is a bit hard to judge for a newly created starter. My best suggestion is to use trial and error and maybe bake 4 hours after knocking instead of 8 next time, and the time after that adjusting with a smaller increment in the right direction depending on whether the bread turns out overproofed or underrisen.
In making bread or pizza dough, there is no step called "leavening."
While there is some variation in method, depending on whether a preferment is used, in general, the active culture (whether it is sourdough starter, commercial yeast, or a combination) is added very early in the development of the dough.
The dough is then kneaded to develop gluten structure, and proofed to allow flavor to develop. This is normally described as allowing it to rest until it is doubled in bulk.
Then, it is "punched down", deflating most of the rise that happened during the proofing stage, and shaped into its final shape, and possibly placed into a mold or form. It then rises again to a greater or lesser extent before baking begins.
There is no before or after the leavening.
Best Answer
Yes, preparing discs of dough ahead of time, separated by parchment, wax paper or clingfilm does work. The biggest risk is that the dough tends to dry out a bit, so keeping the whole mass wrapped up in clingfilm and possibly in wide closable containers may be worthwhile.
I don't know how long it would take you to pre-portion 20 pizza doughs; I'm not super-efficient on that yet so it would probably take me a good solid hour. That might be short enough so as not to require additional retardation.
Most pizza joints at least pre-portion the balls of dough, and they let them relax at (oven-) room temperature, so that they're easy to stretch.
If this is a casual party with friends, rather than a formal dinner or a catering gig, though, you may consider involving your friends to do the work; they may appreciate the social aspect of throwing/rolling dough together (depending on your technique preference), and even topping the pizzas themselves, with your guidance. You may want to make a bit of extra dough to accommodate errors.
I've actually been to an event where everyone brought their own preferred dough recipe to test it out on a wood fired oven, which was a leisurely several-hour event with many successes and a few "failures" (or lessons learned; brioche dough doesn't love 700F ovens). We all just grabbed space on the bench when it was practical, and queued up for the oven when practical.
An alternate strategy is to have plenty of dishes out on the table that aren't time and temperature sensitive, and let people nibble casually while you prep. Marinated vegetables, cold cuts, cheeses, bean dishes, etc. Then spend time chatting with each person you're making pizzas for while you prep them, maybe three or four at a time, to tweak to their preferences and whims.