You know, I have never tried letting the dough rise in the pan. Do you think that helps with spring? And it is amazing how well KABF performs with minimal handling - I am also surprised to see such beautiful browning without the use of oil.
From your detailed explanation of workflow, it seems your background in in bread making 
John
John, I really have no idea if letting the dough rise in the pan helps with spring or not, being it is the way I have always done it.
What may potentially help is the use of a pizza stone. With my earlier squares, I just put the pan into the oven by itself. After several batches, I started to use a pizza stone and put the pan right on top of that, allowing my stone to pre-heat at my oven's maximum temperature (550°F) for an hour after the pre-heat cycle brings the oven to maximum temp. My stone typically reads around 575 to 580°F after that hour.
It could be coincidence that getting a better rise was not from placing my pan on a pre-heated stone, but that my competence with making a square pizza had developed enough by the time I started incorporating the stone that I would have been able to get some decent spring at that point, stone or no. But I've used a stone consistently since, so it's hard to say how much spring is attributable to that fact.
There is no oil in the dough or in the container it fermented in. I do put a moderate amount of olive oil in the bottom of the pan, but none on top of the dough. I think finishing the bake under my broiler helps with the browning.
As an aside, my ultimate square pie vision is was confirmed during on one trip to NYC. After eating at Totonno's Coney Island and then DiFara, we picked up a square from L&B Spumoni Gardens on the way to Paulie Gee's. By the time we got to Paulie's, the L&B pie had cooled. Paulie dropped it into his WFO for a fashion as an experiment.....some of the pie got burnt, but the portions of the pizza that were not burnt were revelatory.
I've thought for a few years now of a spring-form pan for a square pie cooked in a WFO....where the pie is initially cooked (no olive oil in the bottom) in a WFO with the bottom of the pan on to set the initial lift, then topping the pizza, removing the bottom of the springform (so only the sides of the form remain for support), sliding a peel under it and finishing the bake in the WFO with the bottom of the pie right on the refractory floor. I think the combination of what we already love about square/sicilian pizzas with the bottom charred like a Neapolitan-style pie and a leopard spotted upper/outer rim could potentially be seriously gangbusters pizza!
