Is standard .375 rifling fast enough? That has got to be a LONG bullet.

I have never shot a buffalo, nor an elephant - probably never will, except maybe a bison with a muzzleloader or a my Sharps.

I would not feel undergunned with my 9.3x62, armed with a good soft and solid in 286gr. weight. In the .375/06IMP, I'd be quite satisfied with the 270TSX at 2,700fps.
I see no need for even the 300gr., nor certainly anything heavier.

The 270's and 300's made the .375 famous, and the 286's made the 9.3x62 famous - both with loads well below what is loaded for either, nowadays. The 9.3x57 today, will actually exceed the ballistics that made the 9,.3x62 famous prior to 1923 - and do it from a Model 96 Swedish action & with low pressure.

I'd stay with the 270 or 300TSX. I was very impressed with the accurcy of the 270TSX at 2,700fps in my rifle - under 1/2" for 3 shot groups - cloverleafs were the norm.