What I'd do? Reduce loads to handle the highest temps you'll encounter in Africa (and as said above, always use new brass for a DG hunt-including PG that tend to get dangerous when wounded-Oryx, etc.) 'Have had similar occur in TX where hunting season temps might be 60F higher than up here. Corrected the situation by backing off a bit on pet loads when heading to hotter climes. Or, you can rely on your crack-shot PH for backup and tape a ramrod to that gun! Q: Was that brass full-length sized or neck-sized? The .375 case in any form is fairly particular when it comes to FL sizing (and it needs to be done, in addition to trimming, due to stretch.) I have loaded the 375 (and nearly all derived from it) extensively. If you don't mind sharing your load...but to me, looks like a brass re-working issue. Only cleaning the bore and not the chamber can do the same sometimes.
This is a mouthful, but often a reloader will get caught up in c.o.a.l., bullet seating depth, etc. (all important,) but they fail to set the FL sizing die up to Completely re-size the Entire case down to the belt-and that can result in what we see, as the case just above the rim/belt is bulged out as a result. This same phenomena can happen (in the chamber-when closing the bolt the case is compressed and bulged) when the case is not FL resized and/or not neck-trimmed to 0.010" under spec (2.840" not the factory 2.850" chamber neck or unfinished brass dimension). 'Just trying to help. Factory ammo in 375 is just fine (much to choose from and your PH will have extra if your airport comes up short.
Shooting over-velocity 375 handloads, at a minimum, will cost you an extra buff, but on the outside, maybe someone's life...(the bullet, which does all the work, has a relatively high SD relative to other big bore slugs, and consequently can wound a 2nd buffalo behind the target. Usually with solids, but it can happen with a premium soft doing 2,800 fps!) 350 gr bullets doing 2,300 fps is the best medicine in that caliber (about 350 fps slower than the most commonly used factory ammo, and even slower than handloads.) "It behaves like a .416." In this case, $30-$100 more per box might save a life. I handload for wildcats out of necessity but have given up wasting time reloading in favor of buying premium factory ammo for common calibers (i.e. 30-06, 300 Win, 375 HH).
Always endeavor to make that first shot count! It cures all ills.