For the time and effort involved, I don't recommend this one bit. But I wanted to give it a go.
While I didn't use a lathe, there's plenty of turning involved. I used a half inch drill. I often clamp it to a bench and put a small clamp over the variable speed trigger. Then I plug it into a foot pedal.
I went ahead with making the top punch part, first, before even planning how to mount it. I figured I could find some way to attach it to one of my surplus dies. Turns out a 3/8" rod can be given a light taper to friction fit into the crimp ring of any of the 9mm/357 family of taper dies. I had a variety of rare-to-never used dies to choose from, and I went with my Lee 9mm FCD. I cut the top off the adjustment stem, so that I can just take out the die when it's full and dump them out.
I would have removed it from the 9mm crimp ring for a photo, but it's seized in there really good.
The bottom part is made from 1/2" steel round. I turned down the OD to 432 to true it up, leaving it full size only where the slot goes for the extra support. 432 is the diameter of the thinnest part of a shellholder. Then I threaded the base to attach a brass ring. It goes into the press like a push through stem.
Because it's for 223, I could turn the button down from a 1/4 bolt and just screw it in from the bottom, so it's infinitely adjustable. The extra bolt sticking out the bottom fits in the hollow in my press. There's no room for a lock nut, but it doesn't seem to need one. This makes it easy to tweak the shape of the button without stressing out about the exact height.
I ordered some 9 thous aluminum, which seems to be the thickness of a Hornady 22 check. But I couldn't wait and bought some 13-14 thous from the local store. It looks like they'll work, too. Now I just need to figure out how to unclog the spout on my lead pot, so I can make some decent boolits. Pardon the atrocity in the photo!