I currently have a stuck case in my .223 die, I need to try the self-tapping screw method. It was well lubed, but the shellholder sheared off the rim when I tried to pull down the ram.
When mine get stuck it is usually on the internal sizing pin. I use lee dies, just loosen the pin and drive it out. Then use a dremel to weaken the case where it is tight, and put it in a vice and pull it out. Like most things in life, lots of lube helps.
When I despair, I remember that all through history the ways of truth and love have always won. There have been tyrants, and murderers, and for a time they can seem invincible, but in the end they always fall. Think of it--always.