Congratulations on surviving the pizza marathon, and thanks for posting all the photos and the accompanying commentary. I thoroughly enjoyed reading everything.
Like Buzz, I wondered about the 9 tablespoons of total oil for 2 cups of flour. I measured out 2 cups of King Arthur all-purpose flour on my digital scale this afternoon, and I estimate that the total oil logs in at around 34%. Interestingly, when I weighed out 1 3/4 cups of the KA flour and calculated the weight of 6 tablespoons of total oil, which I believe represents the experiment Buzz says he plans to try, I got 33.5% total oil. So, unless my methodology and/or math were flawed, it looks like you essentially performed the dough experiment Buzz is planning to try.
I wondered more about the length of the fermentation of your doughs, all of which was at room temperature. Buzz specifies around 8 hours room-temperature fermentation as a typical case. I would be interested in hearing what your dough looked and felt like after a much longer room-temperature fermentation, and especially if there were signs of overfermentation, such as a very slack dough or one prone to tears forming. I speculate that the high percentage of total oil might restrain the rate and amount of dough expansion and forestall the likelihood of overfermenting, but I don't recall ever using such a long room-temperature fermentation with a dough with so much oil. My practice with Buzz's recipes has been to use a combination of room-temperature fermentation and refrigeration, or refrigeration alone, with a 1 to 2 hour counter warm-up before using.
In seeing your dough after you rolled it out, folded it into quarters, and rerolled it out again, I was reminded of a technique I used with Buzz's original recipe to try to keep the rolled out dough in a round shape at all stages. Specifically, I took the dough ball, divided it into two equal pieces, rolled one of the dough pieces out into a first round skin, put the second dough piece on top of the first skin, flattened it, and then rolled it out on top of the first skin, effectively forming a "laminated" assembly. After folding in the edges of the two skins and sealing the exposed edges, I rolled out the lamination to its final size to be fitted into the deep-dish pan. In retrospect, I think it might have been better to roll out the two dough pieces into separate skins (round), superimpose them, and then finish rolling out the lamination to its final desired size for fitting into the pan. Either way, the finished assembly would be round at all times, rather than an oblong or irregular shape that results from trying to roll out a skin that has been folded into quarters.
I also tried a three-skin lamination with cold dabs of butter between the layers. That produced an interesting flaky texture in the crust. My experiments were tried with Buzz's original recipe that uses around 10-12% total oil (by my calculation), so I don't know how they will work with a dough with more than double that amount of total oil (by baker's percent). I offer up these possibilities with the hope that you will experiment with them, and possibly benefit from them and improve upon them, in your future efforts. (BTW, I reported on my experiments on the thread where I have been trying to reverse-engineer Buzz's many experiments to find the ideal Giordano's style deep-dish dough.)
I though I might also mention that for your friend who is allergic to cheese there is an alternative that might be worth considering, should you make another deep-dish pie for her to sample. It is a non-dairy, soy-based “mozzarella” cheese. Soy-based mozzarella is a firm, mild (but pleasant) tasting, vegetable form of mozzarella cheese made principally from soybeans. It looks very much like regular mozzarella cheese, shreds and slices just like regular mozzarella cheese, and can be used on a pizza just like regular mozzarella cheese. It will melt without any significant browning and it will be chewy and almost indistinguishable on (or in) a baked pizza from regular mozzarella cheese. However, it will not be as flavorful as regular mozzarella cheese, and certainly not as tasty or flavorful as fresh mozzarella cheese. In addition to being a dairy-free product, it is also lactose- and cholesterol-free, so it offers clear advantages to persons who are lactose intolerant or are on low-fat or low-cholesterol diets. I have used it in deep-dish pies along with regular mozzarella cheese and provolone cheese and could not detect its presence. I have experimented with a few brands (basic soy mozzarella only, not the ones with other things mixed in) that I found at a Whole Foods store. I have not tried soy mozzarella alone in a deep-dish pie, but with all the powerful flavors in such a pie I think your friend will still enjoy eating it.