How about 375x2.5 Flanged Nitro Express? If you want you can use the full length 405 case with 375x2.5 FNE dies for a "wildcat" if you long throat the chamber, and still use regular 375x2.5 brass as well. This is what I have to do with my H&H double due to it's very long throat/neck, and I load to 3.40-3.50 OAL. You can get 2300 to 2400 with 270 grain bullets and this setup in a strong action at "modern" pressures, and there is a great deal of "panache" as well.

Jim