I agree with rigbymauser! Try to find a pre-WW2 Mannlicher-Schoenauer M1925 in 8x60S. These are marked 8x60 MAGNUM on the receiver ring. As those prewar rifles have a short, 1 turn in 8”, twist , the 8x60S can be loaded as the ballistic twin of the .318 Westley Richards. The two cartridges are hard to tell apart without looking at the headstamp or using a caliper.
Left to right: .318 250 gr soft nose old Kynoch, 8x60S 250 gr Woodleigh soft nose handload, .318 250 gr Solid old Kynoch, 8x60 227gr solid DWM, 8x60 227gr sn DWM, 8x60S 227gr sn FN/Norma, 8x60S 196 gr PRVI handload

My own handloads of a 250 gr Woodleigh in front of 53 gr VV N160, RWS case, CCI lr Magnum primer, achieves an instrumental, 5m from muzzle, velocity of 2330 fps from the 23“ (shortened) barrel of my old M-Sch M1925. The 196 gr Prvi Partizan bullet (cheapest available here) in front of 50 gr VV N140 clocks at 2580 fps from my rifle.
IMHO this is quite comparable to Kynamco’s .318 Rimless ballistics from a much longer, 28” pressure barrel: 250 gr at 2400 fps and 180gr at 2700 fps, see http://www.kynochammunition.co.uk/318.htm
It would be very hard for both hunter or beast to tell a difference.
Here is my old 8x60s M-Sch and it’s latest victim, May 3, 2014:

As you noticed already, reboring alone will not be satisfactory, as the magazine has to be altered too. Finding a spare spool is somewhere in between impossible and unlikely. If you insist on a M-Sch in .318, you may look for an 8x60 with a worn barrel and have that “Freshed out” from .324 to 329” groove. But M1925s in 8x60 were cataloged only as 24” barrel half-stocked rifles, a full stock Stutzen must have been a semi-custom special order item, a really rare bird. M1950s were offered in 8x60 too, but I have yet to see one.