If you are using 4.5 liters of water (4500 milliliters, or 4500 grams) for 22 pounds (9979.20 g.) of flour, then your hydration works out to 45.1%. I have calculated the thickness factors for your three pizza sizes and they work out to 0.132 for the 16", 0.14 for the 12" and 0.125 for the 9". In the U.S., these numbers would suggest medium to thick crusts. The hydration (45.1%) strikes me as being on the low side for the crust thicknesses you seem to be using. I assume that the crust is on the softer side rather than cracker like, because of the gumminess problem you have described. Is that correct?
The updated baker's percents look like this:
100%, Pizza flour, 352 oz. (22 x 16), (9979.20 g.)
45.1%, Water, 4.5 liters, 158.73 oz. (4500 g.)
0.64%, Sugar, 2.25 oz. (1/3 c.), (63.79 g.)
0.67%, Salt, 2.37 oz. (1/4 c.), (67.19 g.)
1.68%, Oil, 5.93 oz. (3/4 c.), (168.12 g.)
0.48%, Shortening, 1.69 oz. (1/4 c.), (47.91 g.) Note: Weight assumes using Crisco
0.18%, Instant dry yeast, 0.64 oz. (1/8 c.), (18.14 g.)
Note: Total fat = 2.16%
Total dough ball weight = 523.61 oz. (14,844.34 g.)
Thickness factor = 0.132 (16"), 0.14 (12"), and 0.125 (9")
I might add that the reason most people who do not like to sheet doughs in advance is because the doughs can be a bit "bucky" (overly elastic) to shape and sheet in advance of fermenting the doughs in the cooler. Letting the dough balls rise a couple of times before sheeting helps but it may be better to do this after the dough balls have undergone cold fermentation. I'm not familiar with the Dover flour. Do you know the protein content?
The picture I am now getting is that you are making fairly thick/stiff doughs with low hydration and using small amounts of yeast (IDY) and salt, pre-sheeting the doughs into skins before putting them in the cooler (I assume they are covered to protect them from drying out), and using pans to bake the dressed skins once they are taken out of the cooler and allowed to warm up.
If my assessment is correct, I don't know if that is the right combination. I am not a pizza operator, but I think I understand dough behavior pretty well. I would personally give some thought to increasing the salt and yeast levels (at least double the salt), doing the sheeting after the cold fermentation, and possibly experimenting with using screens and/or perforated disks. For the dough prep and management, I would first put the water in the mixer bowl, dissolve the salt and sugar in the water (alternatively, the sugar can be added to the flour), add the IDY to the flour (there is no need to proof the IDY), add the IDY/flour mixture to the water and mix until everything comes together, and add the oil and shortening and mix until the dough is smooth. If you plan to ultimately sheet the dough after cold fermentation, you would scale and divide the dough into individual dough balls, lightly coat them with oil, cross stack them in the cooler for a while, and then down stack them in the cooler. They would be sheeted the next day, with or without docking, as may be your practice, before dressing and baking. I would try using screens and/or disks since I have some doubts about using the pans, which may be preventing your oven from fully baking the crusts.
A couple of other points. I would start using a scale, if you are not already doing so, to weigh at least the flour, and preferably the water also. You might be OK using volumes for the other ingredients since they are not that large. I would also temperature adjust the water to achieve a finished dough temperature of around 80-85 degrees F. That should help achieve consistency from one dough batch to another, and should also allow you to compensate for the cold kitchen you mentioned in your last post.