Norma,
You perhaps already know this, but I think that it bears repeating. First, yeast can only consume simple sugars and, second, if sucrose is used as a source of food for the yeast, it has to be converted from a disaccharide to simple sugars, in this case, glucose and fructose. One of the ways to do that conversion is to use warm water. So, to prove the point, within the last hour I conducted a simple experiment. For the experiment, I took three containers, each with 1/4 cup water, 1/2 teaspoon SAF Red IDY, and a "pinch" (1/16 teaspoon) of sucrose (table sugar). The only difference between the three tests was that the water temperatures were different. For the first container, it was 69 degrees F, for the second container it was 95 degrees F, and for the third container it was 120 degrees F. The mixtures in the three containers prehydrated for 10 minutes. So, as a summary, this is what we have:
Container 1: 1/4 cup water at 69 degrees F, 1/2 teaspoon SAF Red IDY, a "pinch" (1/16 teaspoon) sucrose, 10-min. rehydration time
Container 2: 1/4 cup water at 95 degrees F, 1/2 teaspoon SAF Red IDY, a "pinch" (1/16 teaspoon) sucrose, 10-min. rehydration time
Container 3: 1/4 cup water at 120 degrees F, 1/2 teaspoon SAF Red IDY, a "pinch" (1/16 teaspoon) sucrose, 10-min. rehydration time
After 10 minutes, Container 1 showed very little activity. The reason is that a temperature of 69 degrees F was not enough to convert the sucrose to enough simple sugars to feed the yeast. By comparison, Container 2 started to show very noticeable activity after about 7 minutes. It was frothy with foam and active bubbling. So, water at 95 degrees F was enough to cause the sucrose to convert to glucose and fructose to feed the yeast to cause the activity noted. Container 3 started to show noticeable activity after about 8 minutes but it was less active than Container 2. IDY can tolerate a water temperature of around 120-130 degrees if it is mixed in with the flour in a dough formulation and buffered by the flour, but it is not fond of direct contact with water in that temperature range. In fact, there may have been some cell death.
The above experiment shows that heat can be used to convert sucrose to glucose and fructose. So, if in your case you decide to add the sugar (sucrose) to the water used in the soaker formulation, it is perhaps best to do so at a temperature of above about 95 degrees F.
The other thing to keep in mind is that the Maillard reactions require reducing (simple) sugars to provide crust coloration. So, if you decide to add the sucrose to all or part of the soaker formula water, I believe that you should end up with sugar that is more in the form of simple sugars than disaccharides. I am not sure how that would play out in terms of crust coloration or other effects. You would perhaps have to conduct several identical tests where you dissolve the water in one set of tests and add it to the flour and other dry ingredients in a second set of tests, and compare the results of the two sets of tests.
I might add that as the day wears on, the mixtures in the three containers should continue to show fermentation activity, although it may take a while for Container 1 to warm up enough at room temperature to convert more of the sucrose to glucose and fructose.
With respect to the flour to use, as you know the Full Strength flour is essentially a bread flour, with a protein content of 12.6% (
http://www.gmflour.com/gmflour/Flour_SpecSheet/FULL%20STRENGTH%20BL%20BR%20ENR%20MT.pdf) whereas the Kyrol flour is a high-gluten flour with a protein content of around 14%. Both types of flour can be used to make NY style pizzas so it comes down to personal preference for the most part.
Ceteris paribus (to borrow that expression from one of Craig's recent posts

), the Kyrol flour should provide a bit more crust color and crust flavor because of its higher protein content. The crust might also be a bit less tender than a crust based on using the Full Strength flour, because of the higher protein content.
If the "whole enchilada" method poses a problem from a storage standpoint at market, then you might go with one of the regular soaker approaches. I suggested the "whole enchilada" approach mainly to simplify the preparation of the soaker. I also wanted to see if the "whole enchilada" approach behaved as I thought it might based on my analysis of the scientific principles involved. I am happy just to know that the "whole enchilada" approach worked and was not a complete, or even a partial, failure.
Peter