Have a bench vise? Lightly hold the die in the vise. Put pliers between the die body and the case. Don't grab the deprive stem with the pliers...just enough to catch the mouth of the case. Tap the pliers with a BFH lightly to back the case off the deprime stem. Maybe?
What brand of die? Give the manufacturer a call and they should be able to send you one, or better, a couple of pins. They should only take a couple of days to get, I have 2 spares for each set of dies I have.
I would use the dremel to cut the 38 case. You should be able to do that without damaging the expensive part. Then the fun begins with the 327 case. Keep us posted.
I bet you inspect your cases a little more closely from now on....
Carbide die? Just grab on to it with pliars and put a torch on it. The melting points are about 1000 degrees apart, so I doubt you'd hurt the carbide. And even if you do, it's just the pin.
WEll this stuff happens to anyone who reloads any at all at some point in their reloading life. After several panic attacks, Going in the house setting down and not being able to get your mind off of what you just did. Go back and decide to one way or the other get this fixed.
Avoid sledge hammers.
I would take the advice of an earlier post, place the die in a bench vise. Hopefully you do have one. If not, Remember that bit on the movie Planes , Trains and Automobiles when Steve is at the rental car desk without his paperwork. Your --------!
But back to the die in the bench vise. Take some penetrating oil, squirt down inside the case that has the sticking problem and let it set for a while. Be patient,
BUt waiting on this is worse than watching grass grow.
Then go out and tighten that die as much as you can. The take vise grips. Hope you have those to.. If not stop reloading and go to the hardware store. But a bench vise and vise grips bring them home and install the bench vise.
Grab the case with the vise grips and tighten then just as much as you can and try to move the case. If it moves work it back and forth slowing and gently as you can but with enough force to remove the stuck case pull it off.
Then go in and watch TV, marveling at your ingenuity and relax.