One more vote for the Federal #215 Primer, when making your .375 H&H hand loads.
However, the above only applies if you're not suffering from Velocity Madness and therefore willing to keep your powder charges at a sensible and tame level.
I do not care for "hot loads" in any caliber but, if I did like them/load them, I would be very nervous about the #215 primer possibly causing pressure spikes, especially in hot weather or, when firing multiple shots in a row, thereby heating the barrel/chamber up, such as at the rifle range.
That primer was I think developed for the .378 Weatherby and so, in theory appears like it might be a bit hot for the H&H version but, it does not seem to matter for my admittedly low velocity loads (300 gr round nose, soft or solid, at 2400 fps).
With this primer, IMR 4350 powder and 300 gr bullets, firmly roll crimped in the old H&H, I have experienced my best accuracy in the several bolt actions, plus one single shot (Ruger) and one double (Merkel).
If you get a chance, read Dr. Robertson 's must read book "Africa's Most Dangerous", especially Page 103, first paragraph, wherein he concludes that the .375 H&H, firing a 300 grain premium soft point seems to perform better on buffalo at about 150 fps BELOW factory ammunition standard velocity.
I'd like to say that great minds think alike but, I have only shot one buffalo, whereas no doubt he has taken hundreds at least.
Furthermore, I did not even use the .375 caliber for my meager one buffalo so, I am not worthy to compare my experiences with his in any way.
I can however say that this load has proved quite accurate and also, super effective on antelopes and piggy wiggy, not to mention easier on the shoulder than factory standard 300 gr loads are (I'm a recoil sissy so I would know).
Blah, blah, blah.