Mini-lathes can handle O-1 tool steel no problem and the working surfaces can be hardened and normalized without much drama.
Studying this some more, I think the design we're looking at would be much better suited for an arbor press. I just don't see how there will be room to run the cutting stage near press cam-over due to needing clearance for the material strip passing through the slot. The challenge with flipping the setup over is drilling a long punch for the press ram all the way through (tough material, probably need to drill at least 2" through, likely 2.5") and then finding a way to make the gas checks fall out the bottom of the punch and not scatter everywhere. A slit window would help show when it was full and would be taken off the press ram and dumped.
If swapping ends, the punch could be machined with a simple rim to fit a common shell holder like .223 or .30-'06 and that would serve as a stop for the checks at the bottom as well. The top could be made in two pieces, the cutting/forming piece with the insert would be at the top and a plain threaded body on the bottom. The two could be joined with a standard 7/8" NF nut that had a window cut through it. Thread the top and bottom die body pieces together until the desired clearance is achieved between them and lock each in place with a thin jam nut. This would eliminate slitting the die and make it possible to produce a much finer, polished cutting edge for the discs.