The Hornady 220 gr flatpoint will do fine...the 225 gr spitzer was actually produced for the .376 Steyr....it's worthy of serious .375 H&H velocity...the 220 flat point is designed for much slower velocity

I saw a ruger #3 in 375 Winchester that had been converted to 375 H&H at the Austin Texas gun show last year.

I've got two .375 Winchesters. One is a Marlin lever gun the other is a Ruger No. 3. I've loaded some 235gr. bullets for the No.3 and got great accuracy from them. For the lever I load a Hornady 220gr. Have not actually shot any of them out of the No.3.