Using a hockey puck-turned-armorer's block, a punch, and a mallet, I've unfolded the sides of jackets. Stick the bullet base first into the center hole of the puck. Using the punch and mallet, tap it into the hole, forcing the edges of the jacket back up towards the nose. The rubber of the puck won't mess up any IC on the jacket, and the punch is only hitting the lead core.
Does the core seem like it could be wiggled out of the jacket?