I have a model 1908 Mannlicher-Shcoenauer rifle in 8x56 Mannlicher Schoenauer.
I find it interesting that you have one in 8x57,as mine was at some point stamped "8x57"
The M1908s are 8x56 in most all cases.
The Mannlicher Schoenauer cartridge is not the common 8X56R Austro Hungarian service round, it is rimless and very similar to its German cousin using a .323 bullet.
I shoot mine with cases formed from 8x57, they will not feed through the Schoenauer
rotary magazine until fire formed on the first loading,the precision ground rotary follower is that close.
I simply neck size the case in a 8x57 die after that. Then the rifle performs flawlessly.
I suspect that sometime in my rifles life it was taken over international borders, and many countrys require the caliber to be stated on the rifle,and some clerk did not understand the differance between the common Mauser and the proprietary Mannlicher round.
Your rifles caliber will save a lot when it comes to brass,I paid 100 dollars for 100
cases some years ago.
Best Regards,Creosote