I don't agree that dies can't cause an excessive headspace issue by bumping the shoulder back too far. Back when I first started reloading bottleneck cartridges, I started with a set of Lee dies. I set them up as per the instructions. On my third reload some of my cases starting showing the tell tale signs of separation. I got a case gauge and found that setting the dies up according to the instructions have me bumping the shoulder back way too much. I now set up my dies using a case gauge.
I use a fired case to get a measurement and then set the die to bump the shoulder back a few thousandths.
Anyway, you have to watch out for that 5.56 brass. I don't know where you got it from, but I got some a while back and found that some of it must have been fired out of a SAW or something because they were expanded way beyond what they should have been and were more difficult to resize. This is just the conclusion that I came to after having a couple of separations with that batch of brass.