RE: primers pushed out
Try partial resizing without touching the shoulder of the case, that will eliminate a headspace problem. However, I don't believe that is the trouble to begin with. A case that doesn't reach the shoulder of the chamber will allow the primer to back out, but then will press it back in when the case elongates under the pressure of the expanding gas. That will tend to flatten the primer, sometimes completely overfilling the primer pocket. I'd bet on soft brass or loose pockets first.