I believe one has to trim and set the shoulder back to make 8x56 M-S (not rimmed!) from 8x57. If true, then 8x56 chamber would be too short to chamber an 8x57.
If you have fired cases from when you shot it before, just use a mike and compare to unfired cases. Or fire one shot of same cartridge and use it for comparison.
8x56 base and "rim" are .465, .470 and .470, .473 for the 8x57.
Good luck. Beautiful rifle - you did good. Pat