If I was building a rifle like that, I'd decide on the weight and barrel length I wanted, then after subtracting the action, stock, mounts and scope, I'd work backward with one of the barrel mfg's contour calculators to determine the contour.
I've often thought about the .375 H&H as well. But I thought about a bit different direction. I always figured, since it would be for dangerous game, that I'd get a heavier contour and shorter barrel. I figured a 22" barrel with heavy enough contour to get me to 10-11lbs and a low magnification 2.5x10 Nightforce NXS would be just about perfect. You can get a little better than 2500fps with a 300gr bullet and 22" barrel. It would be nice to carry and handle in tight quarters. It should also be really stiff and be plenty accurate and hit with authority out to 400yds.
AJ