Have you tried Sierra Gameking bullets? In my humble experience, they are very very soft. Are you absolutely determined to shoot a 300 grain bullet for driven hunts? There is a 200 grain Sierra that they recommend not be driven faster than 2200 fps in a .375H&H because of the rapid expansion. I believe the bullet design parameter was for the .375 Winchester, which is a pretty anemic cartridge compared to what you are playing with. Maybe there are other heavier bullets for the .375 Winchester you could use if the light ones are not to your (or more importantly to your rifle's) liking?

Another thought: have you considered cast bullets? You could have a mould made and cast your own at the desired weight out of soft lead. If you drive them at a sedate velocity, they would expand very nicely at lower speeds, and you could retain a heavy bullet. If nothing else, it would give you more things to experiment with.