I have a total of six 375's of various flavors the 375 H&H making up 4 of them. I'm now working on building a 375 Raptor. I found early on to stick with the Barnes TSX or TTSX, and I prefer the 300 grain. They have never let me down. I find I can easily go the 60 round to 80 round country import limit or airline weight limit without any really effect on groups or zero.
Remember you are not looking for MOA but MOBuffalo! The one exception is that Croc. there you need to hit a small target, but the range should be close, 60 to 75 yards with the 75 yards being LONG.
I do have one 375 with a 26" bbl. that will hit your velocities, but all prefer 2500 to 2550 FPS. It has been said more than once that a 375 H&H moving a good 300 gr bullet at 2500 fps is all your ever going to need.
It is a fact that if you juice of the velocity, the fouling will also increase. I also use Wipe Out only and I stay away from the more aggressive Barnes, Sweets etc. After the patch no longer come out blue, often after several treatments I will use Hoppes # 9 to get the last of the powder fouling.
I build my own rifles using almost exclusively ER Shaw barrels and some McGowen. I have found that after break-in they all like the Barnes TSX.
As has been stated here always foul the barrel with several shots before departing. If your PH is any good he will insist on a sight-in........ if for no other reason then to check YOU out as much as the zero. That is to see if you handle the rifle safely and competently. But don't wait for that, 4 or 5 rounds at the range before leaving will do the trick, and I believe is a must.
The bullet is the cheapest part of your trip, even a very expensive premium, and while there are for sure cup and core bullets like Woodleigh, Swifts A Frame Nosler partition and Accubonds and the Barnes originals, I have found NOTHING beats the mono.
I have also found when switching to the Barnes Banded Solids with their brass composition , the zero and groups don't change.....so on that point alone, for me it is BARNES TSX all the way.