Drill the PRIMER?? In a live round?? You got to be kidding!!
Yes, maybe, slowly, but only with a hand twist drill so as to not generate any heat. Once a hole is gently drilled in the primer, soak it with water or oil through the hole. Then remove the primer and he's home free!
I had a 7mm TCU stuck once that I removed exactly like this. Once a small hole is drilled (with the hand twist drill), I used a screw to catch the primer and yanked it out (after I soaked the primer).
It usually takes a blow or heat to detonate a primer. I would do it, but only with heavy gloves and eye protection. However, he has an unusual circumstance with the dowel stuck in the barrel that makes things a little dicey. The live round that I removed didn't have an obstruction, so the chance of things getting ugly were less. Granted I wouldn't want to detonate a primer with or without the dowel stuck in the barrel.