Drill a hole and tap it out to 5/16" - the take a 5/8" nut and set on the end of the die over the case with rim pulled off. Take a 5/16" cap screw with a washer and screw the cap screw into the base of the case till it is pulled out.
There was nothing wrong with your die. All 99 chambers are bad oversize and produce a bulge that makes it hard to resize. Lube the case, push it in part way, pull out and relub may have to do it again.
The very best lubricant I have found is a product sold by dealers who sell PVC underground pipe that use a rubber gasket to seal the joint. It is water soluable and come in different size containers but the quart size will last alife time. I'll try to remember tomorrow and get the name and post it here. riceone.