Is the 300g Barnes not available? The 300g TSX works very well in a 375HH. Barnes have pretty close to 100% weight retention and therefore tend to do well at lighter weights than traditional bullets. The traditional weight in a Barnes is already plenty heavy. The 300g TSX is a really good bullet in a 375HH.
There is a heavy-for caliber fad going on right now. In some cases it makes some sense. A heavy bonded lead bullet that holds together might well expand more and give a better wound channel; It may penetrate deeper than a standard weight bullet. May work better. May. A TSX already has all the penetration one would want out of an expanding bullet- it you want or need more, it is time for a solid. Will it expand more than a regular-weight TSX? What benefit is it purported to have and is that benefit actually useful? It doesn't really matter if it penetrates better if the 300g already exits. And unlike on plains game, where you tend to shoot and let the bullet do its work, on buffalo, you tend to want to put in additional shots. If you are in a herd situation, an exiting bullet quickly becomes an exciting bullet.
Finally, TSX bullets generally like velocity. A TSX of any sort is a long bullet for weight. A 350g TSX will be really long for a 375 bullet. I haven't loaded them nor do I have any interest in loading them, but does a 375HH have sufficient case capacity to get good velocity with that bullet? What other than additional recoil is it bringing to the party? A 378 Weatherby could probably make great use of it, but I'm not sure what specialized use case would make that the best choice on buffalo.