The upper die (punch) is held in with a 5/16 fine thread bolt 2 1/4"long. Do you have the threaded piece that fits in the top of the press?
The CH uses a 1 1/16" dia shaft threaded 18 tpi in the top of the press. The Luger press uses a 7/8 14 threaded shaft. The CH has a 1/2" hole through the center with a tube 1/2" OD x 5/16" ID to shim it down for the 5/16 bolt that secures the top punch. My Luger press was missing that shaft so I made one from a piece of 7/8 x 14 and drilled a 5/16 hole through the center.
I suspect my Luger American is the one that Herter copied.