Pizza bulk fermentation vs proofing (2nd cycle)
I honestly don't really see much of an advantage in splitting into separate dough balls for the second 24 hours of refrigeration.  It sounds like OP is going to take the final dough balls out of the fridge, let them warm up some, then shape, the rise until ready to bake.

My standard pizza recipe tends to be retarded in the refrigerator for 1-3 days, after which I remove it, split into balls, let rest, then shape, then rise a bit at room temperature until I'm ready to bake.  I've tried recipes that required me to separate the dough first in the fridge (or to do it as OP does, in the middle of the refrigerated part of the process), but I've never seen an advantage to it in the way the dough behaved.

The only advantage I can see of splitting into dough balls after the first 24 hours is then after day 2 you can just remove the number of dough balls you plan to use for one pizza bake.  You could potentially let others in the fridge for more time (even a couple more days) until ready to use, or you could even freeze some of them individually for future use.  

If you're not planning on that, or planning on baking basically straight out of the fridge (which I don't recommend), there's not a strong advantage to splitting dough into smaller pieces early.