My goal is to give the NUC it's best chance of building to at least a full deep box before winter. i don't mind starting it now and feeding if the extra time improves their odds.I have done splits/divides before, during and after dearths....it's just a matter of what your goals are and how much you want to feed them, IMO.
i imagine you mean in one double deep, or in two deeps.you are in the south, but here in the north, i would want that nuc in two double deeps come winter.
Question is this why you suggested I should do the same when I get the replacement nuc? What will shaking them on to the ground do? Wont they find their way back to the hive?Make your split now and shake out the laying worker bees 6 feet in front of the split. That will give them a quick boost of bees. Move the queen with the split and let the original location raise a new queen or introduce the bought queen there.