very clever from Dave to have such a ultra rare die set on stock. I had not thought that someone would need this die again in my lifetime. Dave its a good guy and allways fun to deal with him.
I would go with the 12,3x62R Gründig designation. we dont know it any better!
its a unusual length for the mauser case. we know that there were over 100 different cases, sized up and down, cut it to every length possible. but only a few cases exist with 70 mm long brass. I found this with 11,5 and 12,5mm bullet diameter, also a 12,4x50R, but no case with a 12,3mm diameter inside.
with a second DR now we can say it was a Gründig caliber. in this time any german ammunition maker was able to make Gründig the brass on demand. I am sure that he was loading ammuntion in his shop. butllet had have a sometimes very oversized "stopring" on top like here in this pic the first example: 18mm bullet diameter and 18,5mm "stopring" diameter

this large diameter ring was laying against case mouth when loading for giving the cartridges a constant length.
reloading die set were not overcomplicated in the old days, here is a german die for the 9,3x57R 360 ( with a 360 BPE coiled case. I would not wonder if the bullet diameter above the case was 12,5mm or bigger.

its no problem with modern brass and blackpowder pressure if the chamber s a little bit to large I suspect. they dont see such problems in the 19.century and it probably wasn't. it start with high pressure nitro loads.