I e-mailed Berger a few months ago to enquire about the progress of their .375 bullet development. I was informed that the project has been shelved while they deal with the spike in demand for their existing products. If we ever actually see such an animal, it is most likely years off. My concern with the Berger bullet is that it will be developed for the Cheytac class cartridges, like the Sierra 350g SMK was. I would like to see them produce something in the 300g class that will stabilize in a 12 twist barrel and work in the .375 H&H class cartridges up through .375 RUM or .378 WBY.
I have done some limited shooting with the 350g SMK. It is a BIG bullet with lots of bearing surface and a seemingly thick jacket. It will take a BIG case to push it fast enough to be useful in the hunting fields. I doubt very much that it would expand well at all, considering that it was designed to be launched around 3200 fps for specialized military applications. OTOH, if placed properly, you might not need a lot of expansion?
At the moment, the only true LR/ELR bullets useful for hunting, and made in .375, are being produced by Cutting Edge Bullets. Their MTH line offers high bc bullets suitable for the various .375's from the H&H on up. The drawback is that they are expensive. I have been looking for a cheaper alternative for long range practice, but there is currently not much available.
For hunting purposes, the Sierra 300g Gameking will produce a trajectory very similar to a .308 175g SMK if launched at .375 H&H velocities. Like the .308, it will start to run out of steam around 700 yards.
Supposedly, the Nosler 260g Accubond has about the same bc and can be driven much faster. Given Nosler's well known tendency to overstate bc's by a significant margin, I am not sure what kind of performance that bullet would produce. The Barnes 250g TTSX/Hornady GMX have .430ish bc's that could allow for a bit of reach if they were driven fast enough, though I don't think either one would be likely to perform well much past 800 yards or so.
Those are the best options I know of at the moment. You can shoot the expensive stuff that will give you quite a bit of reach, or you can shoot more conventional bullets that will put you roughly in the same class as a .338WM in terms of range.
It's frustrating that there aren't better bullets available to take advantage of the .375's potential. That's a hole in the market that I would like to see filled, but that is where we are at the moment.