Unless I am mistaken, I believe that the choice of a 375 Wby. will jump you out of your price range quite a ways. I thought the Weatherby DG rifle jumped to way over $2000 and to convert a 375 H&H to a 375 Wby. would move you out of your price range also.

My only suggestion is that my 375 H&H shoots under 1 inch at 100 yards and it works for me. The Brownings may be a little lite weight for caliber. Winchester is the classic African DG rifle.

Either caliber will work great for you. You just may have to rethink your budget.