from your description of the chamber and case length measurements it may have been a chambering for a paper patched bullet, I have played with paper patched bullets in several German single and double rifles the chamber necks were all opened up some just before the throat, Some more than others, Most bores were .002 to .004 over also. So .005 may not be to much of a stretch
404 B-J Express is the closest in nomenclature but shows bore of .411 made from 375 H&H is the closest I found to your descriptions there are a number of .416 bore cartridges that are closer to the dimensions you have but they do not come close in nomenclature most made from 375 H&H some from 458 Win Mag what is used to make a .416 Taylor
Do you have a fired case, I would like to see it if you do
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