My advice is to buy a .375 H&H, lay in some ammo, or reload, and shoot often (monthly or twice monthly). and Don't Look Back.
Learn to shoot this type of rifle. It's not hard. 20 rounds a session is plenty, once you get used to it.  A nice fitting rifle helps.  I would look at Winchester M70 Alaskan, or Safari Express.  An Interarms Whitworth is a nice rifle with a slim stock that fits me well.  They are a value.  They come up for sales a few times a year.  The .375 H&H recoil is  about like a 12 gauge 3" buckshot. 
 The recoil, to my shoulder sensor, is about 25% to 45% more in the .416 family:
(Remington, Rigby, Ruger et al.)
Always true:  A LOT depends on fit, weight and balance.  A nice fitting .375 H&H will become your favorite rifle.