Out of curiosity, I went back to my Nancy Silverton book Breads from the La Brea Bakery since I remembered that she gave a recipe for making sourdough bread. Somewhere along the way, I converted the recipe to baker's percent format and noted the numbers alongside the recipe. The number that stood out in my memory and that prompted me to go back to revisit the recipe was that she used a natural starter culture (preferment) that was about 30% of the total formula flour. I believe that figure is a bit less than what you used for your "accidental" dough. From my notes, I also saw that I calculated that the preferment was of a consistency very close to that of a classic poolish (it was a little bit wetter). The total formula hydration was 60.9%, and the salt use was 2.2%, both with respect to the total formula flour. As you can see, apart from the preferment numbers, this set of numbers is close to what you use for your basic Lehmann NY style dough formulation. From the instructions that accompanied the bread recipe, after the final dough was made, it was subjected to a room temperature fermentation at about 70-75 degrees F. The dough doubled in volume in about 3 1/2 to 4 hours.
Ultimately, the dough went into the refrigerator for a cold ferment. However, and here's the rub, Ms. Silverton said to cold ferment the dough for 8-12 hours and no longer than 24 hours. That suggests that it is unlikely that you will be able to use an Ischia preferment that is over 30% of the total formula flour and have the final dough fit within the timeframes you now use at market. You can conduct a simple experiment to see if this is the case, and maybe it is worth trying, but I suspect that you will have to use considerably less than 30+% Ischia preferment to have the dough make it through almost four days of cold fermentation. Fortunately, you at least have the preferment dough calculating tool to be able to easily come up with the numbers for your experiments. Maybe you can try using something between the two values you used for the Ischia preferment to see if that gets you headed in the right direction.