I work in Africa as a PH and have used a 375HH for 20 years now. I have had near 100 clients hunt with this cartridge as well There is no better rifle for the whole world then the 375HH just as it is. Sighted 2.5" high at 100 yards with the 270 grain bonded bullets, it dead on at 250 and 5 inches low at 300. For the intended species what more could you ask for? When you switch to the 300 grain bullets they are a perfectly zero'd at 100 yards making that the thumper load for the big stuff.
I have seen the biggest animals walking the earth shot with a 375HH from Brown bear in Alaska to Elephant in Africa. Not a single one has been lost. This is the one gun one planet match the has kept it so popular for so many years. No other cartridge gives you as much killing power for the investment you make in the recoil. A good friend of mine Saeed AlMaktoum has a 375 loaded into the 404 case. His velocity is 300-400fps faster then the standard HH design. He has killed more then 80 bufflao, a dozen elephants, hippos, and plenty of other African game. He is downloading it to slightly more then a factory HH cartridge. Reason? The bullets perform better and the extra velocity caused too many erratic bullet performance issues. If you want another 100fps with the stock HH cartridge shoot a 26" barrel and load them a bit hotter then factoy. You will see that 2750fps with the 270's and 2600 fps with the 300's is more then you will ever need.
It's old and boring and it seems like everyone and thier dog has one. That's because it works so good. Let me put it this way. I own only two hunting rifles, ........and I do this for a living. One is a 30/06, the other is a 375HH. I have never wished for more power or a flatter trajectory from my either of hunting rifles.