I used standard 8x57 Mauser RCBS dies to load 8x56M/S.
It's been a couple years since I've fooled with it, but it worked out OK for me.
I took a Lyman shellholder (because it was handy) and turned it down thinner so it would shove the 8x57 brass in further to set the shoulder back as related above.
The brass needed to be thinned a bit at the base or it won't chamber in my rifle. I expected that from the dimensional drawings and it takes very little to accomplish.

Standard .323 8mm bullets, neck sizing after the first load to preserve the case being blown out to the chamber. I'm sure the old 8x57 shoulder being set back doesn't perfectly match the 8x56 but if you're careful you can get a gentle crush fit on the closing bolt to maintain headspace on that first firing.
After that neck sizing only keeps you there.
I was using a 32acp seater die to neck size,,the outside diameter seemingly just the right diameter for the job.
Once I had the 8x57 FL die set just right for making 8x56's from 8x57,,I didn't want to re-adjust it for necksizing the once fired 8x56 brass with their properly shaped shoulder.

Then after all that I found a nice set of real 8x56MS dies.,,and have never reloaded any more up for the rifle since.
Time to get at it I guess.