John, nice looking pie. There is a lot of different things we are talking about here so let's see if we can keep them straight.
1) Reballing before or after bulk fermentation
2) Reballing (gluten development) of high hydration doughs
3) the mass effect
4) the effects of lengthening fermentation (independent of temperature)
1) I'm not sure if reballing of the dough is specific to the Reinhart formula or if it will change the Lehman dough. The perspective that I take is that dough is dough. We like to give them names but they don't really care what you call them. They do however respond to what we do to them in the same way universally. Reballing serves one purpose, it builds gluten strength. It does this for any dough out there regardless of the formulation. As you know, it's also used widely in the bread world.
As far as when any dough is reballed before or after the bulk, yes it does make a difference and has a different effect on the final outcome of the crumb. To see the effect, all you have to do is make a batch of dough enough for 2 pies. Ball one right after mixing, and ball the other one after a lengthy bulk ferment or after it has risen 25-100% (your choice here). And yes, time or rest periods and more specifically fermentation builds strength in the dough (biochemically or whatever Scott123 wants to call it
2) High hydration doughs are slower to develop gluten, especially if using low protein flours. They require more mixing and techniques such as folding, (re)balling, and rest periods in-between to properly develop the gluten matrix. The higher hydration and lower the protein content, the more of these steps you'll have to take develop that dough. Therefore, (re)balling, (re)folding, rest periods are used with purpose and as needed dependent on if the specific dough in question requires it or not.
From what I have read on this forum, reballing in general, and specifically after bulk fermentation is a no no for the NY style. It's not "traditional", and the NY styled doughs may not handle it. Why? Because the style gravitates more towards higher protein flours, moderately low hydrations, over mixing, and oil to achieve that unique crust. But if you up the hydration, or lower the protein content, or cut down on the mixing, or cut the oil out, the game is changed entirely. Do I personally reball after bulk? Yes - the heck with traditions. I do it because my dough, like yours, needs it.
3) The mass effect has been discussed before, but basically the bigger batch of dough will ferment faster than a smaller batch b/c the bigger batch stays cooler longer. So when making LARGE batches of dough, you may need to decrease the yeast to about 80% or so of what you normally use. I think I saw a video or read some post where Tom Lehmann gives a great explanation of this.
4) Effects of lengthy fermentation. There is a lot to discuss here so bear with me. I don't have all the answers but will give you my take on these topics.
I'm thinking I have a theory that might possibly be correct....in the case of high hydrated doughs, the dough is so loose and hard to handle, that the act of balling them after mixing does very little to build strength in them. After they sit in the fridge for a period of time, the acids from fermentation strengthen gluten bonds...which makes them much easier to handle and much easier to ball (reball), which in turn builds more strength. And as for the bulk fermentation of high hydration doughs, the more dough mass the faster the fermentation, the faster the cycle above occurs.
John, you are correct (generally speaking) that balling a high hydrated dough immediately after mixing may not be enough, and that dough may require another reballing after a rest period. I think what you are experiencing here is that you are reballing the dough cold after it has rested in the fridge. Cold dough is usually easier to handle then room temperature dough, especially when dealing with a high hydration dough.
Now, if you were to allow that dough of yours to reach room temperature, it may in fact be much harder to handle than before! Why would I say that as this seems contradictory to what I stated in 2). What happens when dough sits for any length of time, is that enzymes break down the dough making it more extensible and soft. This happens more readily in higher hydration doughs and at higher temperatures. This is why if you want to work with a long fermentation dough, it is a good idea to decrease the hydration by a few percentages or accommodate this effect.
In some of my earlier experiments with an high hydration dough (AP = 70%+, BF >73%, HG 80%) and long fermentations of 3-5 days, the dough would turn almost into a liquid!
Anyways, not very scientific, but this is what I have observed in my dough making.