The 375 does less bloodshot damage than say a .270 or .243 so whats the problem..unless your using some kind of a bloody soft bullet thats exploding...

Try a flat nose solid or cup point from Northfork or a GS customs from RSA, even a 350 gr. Woodleigh makes since..I have shot worlds of plainsgame with a .375, 416 and 404 without meat damage..