Use of a small base sizer die may cure the problem if it just barely fits now.

If they don't make one in 7x57,,I think 30-06 is available and would do (I think!) so as just to be able to swage down the bases a bit to function w/o difficulty.
You can always turn down the bases a couple .000. I've done them with nothing more than a sharp fine cut file, a couple swipes while the case is spinning in the drill press. It's not a drastic alteration.


Maybe Barrella used the 8x56MS case to make a 7x57 on. They have the very slightly smaller base dia but the rest is 'normal'.

Nice rifles!!