pulling bullets
Another approach is to use your press. Put the round into the shell holder and raise it until the bullet protrudes. You can use pliers to grasp the bullet, and then lower the case.
You will often cause some damage to the bullet. However, I have used a rubber band wrapped around the bullet or tape on the bullet, and that decreased the damage. Take your time--apply steady constant pressure.
Obviously, a proper bullet pulling collet would be ideally suited for the job.
Good luck
Therion