My Krieghoff Teck O/U double rifle has two sets of rifle barrels in .458 WM and .375 H&H, both rimless cartridges. However, the ejector works flawlessly on both sets of barrels, to the point that finding fired cases is sometimes difficult. At the time I ordered the rifle (1970), those were the only DG calibers offered. I have taken the rifle on three hunts in Africa and used it on four of the Big Five with no difficulties whatsoever. The problem is no so much the rimless cartridge, but the question of ejector vs. extractor.

Incidentally, the present day Krieghoff S/S double rifle has the same manual cocking arrangement as your single shot, except that after the first shots are fired, the rifle automatically cocks itself when the action is opened, so that no further manual cocking is required, which seems like a very sensible feature.