my last correspondence with Collath 500 BPE before he was surprisingly dying in 2009 ( you will find him here in old mannlicher forum post) was going arond the Mannlicher Schoenauer Modell 1912 in 10,75x57. Collath had told me that he have known 2 or 3 M 1912 rifle's in austria. he was then on a trip to vienna were someone had offer him such M 1912 but in the end it was a worn M 1910. He had no pics from such a beast and to my knowledge nothing floating around. in all we know it must be engraved Mannlicher Schoenauer M 1912 on the receiver.
have heard that Erich Schoeder http://www.eschoder.com/english/english-index.htm
also confirm the existence of the M 1912 in 10,75x57.
it's the only good explanation while the 10,75x57 is sometimes called 10,75x57 Mannlicher. cartridge collectors have found it under this name in the Georg Roth list. this designation is wrong

I have a Suhl made M 98 in 10,75x57 and collect informations about this cartridge for year now. my opinion is that the little 10,75 was created in Suhl beetween 1904 and 1907.