I just had a look at George Nonte's Home Guide to Cartridge Conversions. This states that the .318" Rimless Nitro Express (a.k.a. .318" Westley Richards Acclerated Express), can be formed from a .30-06 case; first trim to 2.38"; then run into a 8x56 Mannlicher Schoenauer FL die until the bolt will close. Then expand the neck to hold .330" bullets.

This reminds me that the .318" WR actually does not use .318" bullets. This is the bore size. Nonte records that the .318" WR had a rim and head diameter both of .465" and a neck diameter of .358". It used 250 grain bullets at 2,400 fps muzzle velocity.

If you're interested in 8x57JR, JC Munnell wrote in Precision Shooter, November 2005 about "Some Other Eight Millimeter European Sporting Rounds". This gives favoured loads and bullets for Drillings and doubles. Also he wrote "Sorting Through (Some of) The 8x57 Cartridges", in Precision Shooter, July 2005. He seems to have used only 196 grain (DWM, Norma, S&B and RWS) bullets in his Scherell double rifle, (8x57JR), and both 196 and 225 grain in his Krieghoff Drilling, which was also 8x57JR.