Sorry, but this post has me confused! It reads as though you are more concerned with saving the recapping pin and expander ball than the die!
I tend to have 2-3 stuck cases each year with the volume of 223 match ammo that I load each year. Usually, when a case gets stuck, the run pulls out of the shell holder. When this happens, I back the stem out of the case as far as I can. Then, I break out my stuck case tool, drill the primer pocket, tap the case head, then torque the case out of the sizing die.
Typically, die manufacturers will remove a stuck case for about $5. Between the time not able to reload because the die is in the mail, I have found the stuck case removal kit to be a worthwhile investment!