Ken,
Have you discussed these rifles on another forum? For some reason, your problem seems very familiar. The rifle was proofed in Suhl, and carries both a View Proof(crown U) and Definitive Proof(crown B).This shows the chamber dimensions were correct, at proof, for some cartridge that was for a bore(not groove)diameter of 7mm, with a case length of 57mm. This mark identifies dimensions and not the nominal cartridge. It is happenstance that the numbers match a well known cartridges name, not all do. The most common 7x57, is based on the M93 case, which has a normal head diameter of 12.05mm. There were some made for 7x57 cartridges based on the M88 case, which has a normal head diameter of 11.95mm. There is no way to know which was intended, from the proof marks alone( there is a similar case between the 8x57IR and 8x57R/360, except the proof marks don't match either name). A common 7x57 M93 cartridge made in Europe would be a tight fit in a chamber made for 7x57 M88. Depending on manufacturing tolerances, it may chamber with difficulty, or not at all. On the other hand, American factories often make 7x57 ammo on the 30-06 head diameter cases( even for 6.5x55 which is even larger), which is nominally the same as the M88. Therefore, if the rifle was chambered for the 7x57 M88, it is not surprising that S&B ammo would be difficult to chamber; and as for the Hornady, I believe someone else supplies their cases. If they come from Europe, they may also be M93 head diameter cases. I suggest you try Remington or Winchester ammunition. It is very difficult to make a chamber cast in a Mauser rifle, because of the gap between the rear of the barrel and the bolt face, as well as the cut for locking lugs. After installing a number of barrels in Mausers, I have learned this gap varies and may be .100-.120". Therefore a chamber cast will be shorter than the cartridge, so the measurements may not be at the same location on the case.
Another question you didn't address is the actual nominal caliber of the other rifle. There were actually two different 6.5x54 cartridges. One is the well known 6.5x54 Mannlicher-Schoenauer, and the other is the 6.5x54 Mauser. These are similar in performance, but very different cases. The Mannlicher-Schoenauer case head diameter is smaller than the Mauser's which is the M88 size. Consequently, depending on actual length, neck location, shoulder angle, etc.; it may be possible to chamber and fire a 6.5x54 Mannlicher-Schoenauer cartridge in a 6.5x54 Mauser chamber. It would be extremely rare to find a Mauser chambered for the Mannlicher-Schoenauer cartridge, or a Mannlicher-Schoenauer rifle, chambered for the Mauser cartridge. I suggest you closely check a case fired in your rifle, against an unfired one, to see if it has been fireformed to 6.5x54 Mauser body. I don't intend to insult you, but remember you should feed the Mauser rifles through the magazine. If you just drop a cartridge into the chamber, the bolt will close with great difficulty, if at all.
Mike