On one side it is a question of barrels, NEF makes a barrel for the 38-55 which actually measures .379 so 375 bullets are undersize and won't perform properly. One could use an expander button that is sized for the barrel but then there is the question of bullets, unless one is buying from a maker like Hawk (I'm not sure they make a 379/380 jacketed bullet, but a custom maker somewhere should) one is pretty well limited to shooting cast. One could have a barrel made up or bored out but it would be a fairly big expense.
I too have thought the 375 JDJ would be a perfect NEF chambering, but I would be surprised if we ever saw it. It would be nice if they would just offer a proper 375 Winchester. Then folks could have the best of both worlds, the 375 Winchester ain't no slouch, in fact the 375 JDJ from a 14" barrel is it's ballistic twin, but those who wanted more would have a proper barrel that could be rechambered for the 375 JDJ or the 375-06, a chambering capable of driving 270 grainers to 2400 fps or so, not that far from a 375 H&H.
I have come to the conclusion though that whitetails just don't need that much killing and am beginning to rethink a 308 or 30-06, and even though this is the NEF board I have to say I want a 110 Savage so that a really good barrel and aftermarket triggers and such are just a catalog away.
However, out in North Dakota where you are a 375 JDJ makes a lot more sense than here on Lookout Mountian in Alabama.