Gert...............................great cartridge and great question(s). Will you be able to duplicate the .318 load in your 8mm. Yes, probably. Will you be able to drive a 250 grainer at 2400fps? No, probably not. I doubt that the old 318 advertised loads were ever achieved in a sporting barrel. 250 grainer at 2400fps? That's about all I get in a 338-06 with warm loads. In the old days of light loading for hot tropical hunting, 2200 to 2250fps would be more like it. Having said that, I have never chronographed a 318 from yesteryear. If Westley Richards' advertised loading of 55 grains of powder driving a 180 grain bullet at 2700fps was even close to correct, then their other loading of 52 grains driving a 250 grainer would be about 2220 fps according to ballistic calculator. (lots of variables though) But whatever the velocity, it was probably enough, as it was Wally Bell's favorite cartridge (despite reports to the contrary) so it must have been a real killer on practically anything. You could probably approach 2200 fps with a 250 grainer in your 8X57 depending on your rifle/brass/technic etc. That should do it.
BTW................the old J bore 8X57 that I hunted with as a kid was loaded with a 227 or 236 grain bullet and each with a coarse flake powder with a charge weight of 38 grains. I had no chronograph then-nor did anyone else mortal- but the load and the velocity were modest. We estimated this at about 2000fps, and so added 10 grains of the same powder from a bullet pulled case, and reshot it. The bolt would not open without a mallet. I spent a lot of effort trying to get performance out of this old split bridge Mannlicher without success. Today, you will do better with the S bore, and have fun doing it. A case head failure can ruin even a good rifle, so be cautious.
If you do not have a good source of 250 grainers, PM me........................................................good shooting ....................................FW Bill