The way I saw to pop Berdan primers out was to fill the case with water,
Sit the case on a block with a primer hole drilled in it,
Then push a tight fitting punch into the case neck,
Smack it with a hammer.
The hydraulic pressure pops the primer right out of the case.
Messy, time consuming, but a standard primer will plug right back into the case when you are done.
Drill a straight flash hole in the case and you can punch them with a standard die next time.
Time consuming, Messy, but worked for an old, strange caliber Sharps I got one time with brass, All Berdan primed.
I just pass on Berdan primed cases now, steel or not.
Just too much trouble to get them running.