Never hunted elk or used the 8x57 and it is not an American bullet but Woodleigh tests its bullets with a range of velocities recommended as being effective.

The 8mm 196 gn RNSP looks like their bullet designed for the 8x57mm JS.

http://www.woodleighbullets.com.au/bullet-lists/traditional/264q-333q

There would be bullets in the range of 170 gn to 200 gn designed for the 8x57

Also European bullets for moose, red stag and boar in the 8x57 would also probably be suitable. The cartridge is still popular in Europe including driven game.