I do not think the core theory is correct since alpha made sure to jab in his forehead core when she attacked. If he were all cores that attack would have been pointless. I think she means that once you've grown a breath-right strip it is time to slow down and rethink your life.
Your assumption is half correct. You are right on the fact that attacking the head makes little sense core wise however they have stated that "gray" has a brain and his main "ie first" core in that area. Therefore if she most likely instinctualy attacked the brain to either kill or disable him.
Good luck on the move! Those are a pain in the everything, really. But here's hoping for newer and better things!
oop... the strength is going to go well, but the fact he doesn't have to eat probably won't... This scene's getting interesting!!