I would fetch the tip of the extractor a good rap with brass punch. That's the little wedge shaped part under the barrel, just in front of the barrel lug. If this does not work, then you might need to drill and tap the cartridge and remove the case with a stuck case removal tool.
Here's how I did this once with 7mm TCU that got stuck:
Use a hand twist drill only to drill the primer. DO NOT use an electric or cordless drill, this my set off the primer. Use a HAND TWIST drill only like a tip drill. These are available at hobby stores and welding supply stores. Clamp the barrel securely in a gun vise or use a padded jaw of some sort that will hold the barrel with marking it up. Wear a good leather glove while slowly drilling a hole in the primer. Do this carefully so you won't set the primer off. Remember, it usually takes an impact to set off a primer, so carefully drilling it out should be safe enough. However, stay away from behind the cartridge and wear the glove and eye protection, just in case! Once the hole is drilled in the primer, squirt some WD-40 into the primer to kill it. Now use a screw to catch the primer and pull it out with a pair of pliers.
Now you can go ahead and squirt more oil into the powder itself just as a precaution. Now drill and tap the case just as you would to remove a stuck case from a sizing die. I used a 1/8" bolt and matching thread tap, a socket, and a fair sized washer. Slip the bolt through the washer, then through the socket (the socket must be large enough to fit over the rim of the case, but small enough to push against the breach end of the barrel).
As you tighten the bolt, the case will be pulled from the chamber. As any advice you get from the internet, use at your own risk and descretion! I'm sure that Greybeard would not condone such activity, I'm just telling you how I did it!
