This is why I became a fan of Ken Waters and his Pet Loads. I have had great luck with the top performing combinations he recommended for 30-06 and 300 win mag, 223 rem. Saved me some $, time, and get me off to a good start. I'd start a little lower than his one of his "pets" and work up. But reading his articles and checking other books along the way so I knew where I fit on the pressure & performance scale. He tends to be conservative, not pushing limits as much as Bob Hagel and others did.
CIG - regarding that book you are reading: could be since its talking about Africa, he may be warning that a mild load developed at 30-50 degrees in the US may be close or over max on a very hot day in Africa with ammo baking in the sun. Depends on powders and such but I have read numerous references / warnings to consider the heat likely to be encountered in the field. Now these more modern "extreme" powders and such are less heat sensitive - buy its something to keep in mind.
I usually don't start at the very bottom load in a book unless I have reason to believe that my gun might be sensitive. I might start a grain above the minimum, load 3 and see how they do. Go up a grain or 1.5 and try again, depending.
One thing, that 375 H&H is a big case and I'd doubt you'll see it react dramatically to charge variations of less than a grain unless you are really pushing the max - compared to a 22 hornet or 204 Hornady.
Given its a big whomper round you might not want to pound yourself grain by grain for too long.