In a modern action, the 9x57 will duplicate the .358 Winchester easily, perhaps exceed it slightly, but not much. The case capacities are just about identical and the .358 has close to an 'improved' case design. Due to some of the actions used in the .358, ie: M99 Savage, the .358 is somewhat underloaded to it's real potential, and can be improved upon.

Velocties of 2,350fps with 250gr. are easily acomplished in a bolt .358 Win. gun with 22" to 23" bl. The same can be said for the 9x57 Mauser in a similar bolt gun, ie: 98 Mauser. A working pressure of 60,000PSI is feasable.
I would do that route, but probably improve the 9x57 case and use .358 Win. dies for neck all sizing and bullet seating. The Improved chamber can be cut with any Improved reamer for a standard bolt face, and a neck throater used for that part of the chamber, or a dedicated reamer can be purchased for $160.00(replacable pilots, or much less for a solid pilot reamer. I've had excellent service from Pacific Tool and Gauge - Dave Kiff.

Note the dies must be set so the 20 degree shoulder of the .358Win. die doesn't push the 9x57IMP 40 degree shoulder back - pretty easy stuff for anyone familiar with loading. It should never need any further sizing, than neck sizing.

Thus, the 9x57 IMP should be able to push the 250gr. at just over 2,400fps, possibly another 50fps to 2,450fps in 24" bl. It would shine with the various lighter TSX bullets and standards like 225gr. for about 2,550fps to 2,600fps, but that is a guess. It might do better yet. I was able to get 2,650fps with 180 Speer from a Model 94 Winchester with 20" barrel in the .356 Win. for a fast stepping Deer/black bear load. My preferred bullet for that round, which would easily be exceeded by the 9x57, is 2,150fps.

57mm brass is plentiful - 6mm Rem, 7x57, 8x57 - easy to buy new brass in bulk, cheaply. Much easier than 62mm brass and no more difficult than '06 brass.