I too think this is your chambering. I have chased down several of these in the last couple of months. You can look up some of my posts in the German section above for detailed discussions. A couple of general comments.
- The 9.3/57R - .360 is 15 mm longer than the 9.3x72. This is much longer than accounte for by the 15mm.
- Many of the break action stalking rifles are found in this caliber.
- There are at least three distinct versions of the 9.3x72R, even without drifting off into the Sauer and 82mm versions. It is not uncommon at all to have a chambe that won't seat a modern 9.3x72R Norma case. I bought one drilling on a GB auction. The austion house said that they presumed it was a 9.3x57R since the 9.3 x 72R ammo lacked 1/4" chambering (very similar to yours). I contacted them and asked them to use a new unfired case or a resized clean case. THey did and the 9.3x72 fit perfectly. The old guns are very sensitive to oversized or dirty cases, even to a small degree.
- I bought another drilling, marked exactly like a 9.3x72, but the ammo wouldn't fit, not even empty cases. I neck sized the cases in a 35 Whelen die, and they fit. A lead slug of the bore showed it to be a true .357 barrel.
As a general rule, in an older gun, my first guess would be that it is a tight chamber in the longer version, or it is not actually a .366 bullet. For years, all the ammo loaded used a reduced diameter bullet with a short driving band. These are not readily available any more and you really need to use bullets of the proper diameter, with the neck sized to the proper size.
If it is a stalking rifle, my first guess would be that it is a 57mm case.
Keep in mind too that just because it is modern ammo, it isn't necessarily exact. I recently bought a high grade O/U combo gun with an 8x57R rifle chamber. It was made in Berlin in 1938. New factory 8x57R ammo wouldn't chamber. I tried new 7x57R. Same story. A barrel slug showed a .323 groove diameter. I found that old German military 8x57 form the WW II era went right in (but of course didn't extract). My guess was correct that the old ammo had the correct .469 base diameter. All the new ammo (S&B) was made to the "30-06 standard" of .473. This was true even though it was European ammo. The rifle was made to such close tolerances that it wouldn't chamber the world's # 1 standard case head. To solve it for the future, I took a 308 reamer and just barely relieved the breech end of the chamber to a proper size, and used a small fine stone in a Dremel to relieve the hardened extractor the same few thousanths. It is undetectable except under a magnifier and you can make ammo from any appropriate donor case.
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