When I used to shoot the 350 grain Barnes Originals from the 375 H&H, I used 75 grains
of IMR-4350 and a Federal 215 primer. This will get you 2400-2450 depending on your rifle etc. Some other max loads from Barnes etc. a 350 banded solid and 69.5 RL 15 is listed at 2449, 68.5 of Ramshot Big Game yields 2411. 82 grains of N-205 will run about 2460.
The Barnes 350's did for me, but I shot most of them from my 1-10" custom. I can't say first hand with this bullet, but a phone call to Sierra would give you the answer from the horses mouth. I suspect you might get away with it up close, but lose it down range fairly soon. Maybe someone with first hand info will kick in for you.
Boy, a 350 in a 375h@h... I almost bought some of the Barnes tsx 350's when they came out. I've already got a great load with the 300 tsx and I figure it'll go through a rhino, so why go up in weight??? I'm getting sub moa performance in a 12" twist rem with the 300 tsx.
I'll bet you dollars to pesos that the 300 stx is longer than a lead core sierra 350. I see no reason it won't work, but you may have to go to I 4320 like I did with the 300 tsx to get it to fit. The 300 grain hornady bt also works with I 4320
I'm using a m700 sps limited edition lightweight 375h@h
6x Nikon monarch
rem 375 brass
70.0 I 4320
The "Rhino" 385 grain lead core is suppossed to stabilize in a 1-12 375 H&H also. I doubt that at 2250fps anybody has evaluated stabilization much past buffalo range. The 300 grain TSX should be as adequate as any 375 H&H load on African game. The 350 TSX should do well also. I can't recall how long the original lead core is and my micrometer is broke. If I can borrow one in the AM I'll post some lengths.