Working with the general public a few days a weeks as a commercial gunsmith, I get lots of these stuck rounds to deal with. Gentler is better and that is the way to proceed, but sometimes nothing works and you are the last resort to get things fixed. Now there is stuck, really stuck and @#@! stuck. At level three (often because the customer has already tried his best to remove the rim, has pounded, etc.) you need to resort to the hammer and rod method. The rod needs to be almost bore diameter with a cone shaped (center drill) end to center on the bullet nose and a small outside radius to prevent bore damage. The rifle is placed in a padded vise and the muzzle is pointed up and in a safe direction. Pour in lots of Kroil. Make sure that the primer cannot hit a sharp place on the way out (plug the bolt raceway with something soft). Put on safety glasses and gloves and if you are a pessimist, hearing protection. Now take a large hammer and tap the end of the rod. Tap again. We are looking for good momentum here, not peening blows. Often it will come out with a few light taps. If not, increase the strength of the blows until the rod starts to move downward.. At this point the round may not have come out, but you will have succeeded in driving the bullet into the case (stage 3 stuck). Pour in WD 40, Kroil or other liquid into the bore to help kill the now exposed powder/primer and give it a few minutes to work. Then you can seriously lay on the hammer and things will soon come loose.
This sounds dangerous, but is only marginally so. If the case explodes it will mostly work at blowing itself out of the gun and tearing it's own head off. Some brass shrapnel blowing out at the chamber would be the worst of the scenerio, This obviously would not be good and needs to be protected against, but it is really unlikely as I have done many of these over the years and never had a round go off - there is nothing to ignite the powder except the very shielded primer or an unlikely spark off the rod. I keep my hands, etc away from the muzzle and breech. As a side comment, I also charge the customer double the normal rate for the "pucker factor". If a slide hammer puller with a case head attachment is available and use of freon "cooling" sprays are at hand, give them a try first, but the hammer and rod method always works.
Scott