I suspect the answer may be a 20 bore x 40mm or 50mm. I shortened a 20 gauge Cheddite case to 2" (50 mm) and it fit right against the throat/lands. I took a few .610 pure lead balls and carefully flattened them in a smooth vise until they measured .642. I found a Cowboy Action Load for 20 gauge that pushed 3/4 oz of shot to 1000 fps at around 6000 psi. Since the balls weighed 330 gr (almost exactly 3/4 oz) I loaded 5 rounds with a powder charge reduced 1 grain, used the base of a BP 20 gauge wad as a gas seal and pressed in a resized and lubed ball. I had forced a lubed ball through the bore and it engraved and passed through easily. I measured the ball I pushed through and the groove diameter was .645-.646. I fired two of these offhand at a makeshift target at 25 yds and they functioned well, the recoil is light and they shot to point of aim. This may well have been a 40 mm cartridge, because even with black powder and conventional wadding, the case is ridiculously long at either 2" or 2-1/4". I just ordered some balls cast .648 and some 18 gauge wads which fit the MagTech brass. I will shorten the brass to something between 40 and 50 mm and use appropriate cushion wads to seat the ball flush with the case mouth. I think it will work perfectly.
I did notice in trying the gun that there appears to be be barrel bands around the breech, along with Sauer Suhl, both in Platinum or silver. Also, these barrels ar steel, which I think is pretty early for those.