I have a friend who is a PH in Botswana, and he has a Mod 70 bolt rifle chambered for 458 Win Mag, housed in a Macmillan synthetic stock. It is eqipt with good open sights, and has a 20" medium weight barrel. He had this rifle made for going into the Tsaro bush for wouned Buffalo. The recoil is horrendous, but that thing handles like a dream in the tight stuff. His staff calls this rifle "THE BLACK BITCH", but when they need to crawl into the tight places with a big bull, they always grab the BLACK BITCH, and leave their full length rifles behind.
I think you will like the short barreled 375H&H, and for it's special purpose, will be just right, IMO! I would dearly love to have an 18" barreled double rifle, with good express sights,and chambered for brass 12 bore, hard cast bullet rounds, for just such use!