No, bench-rest shooting with a .375 may not be one of the most popular sports (at least outside of the circle of sickos like yours truly
)
But, believe me, expecting no better that 1.5MOA from your .375 is cutting it a lot of undeserved slack. The .375 H&H (just like its offspawn, the .300 H&H) is capable of (and should be expected to achieve) superb accuracy in the sub-1" region.
I had those results with the many .375 rifles I have owned or shot in the last few years. Ruger, Beretta, Winchester, Sako, Interarms.... All mighty accurate.
As far as price, the Winchester mod. 70 and the Savage Safari Express should fit the bill nicely. Only thing I don't like about the Savage is that butt-ugly (and unsportsmanlike to your buddy hunters) muzzle-brake at the end of the barrel. Aside from that, from what I hear, it's a winner in terms of accuracy and price.
If you get a .375 and you
cannot get any better than 1.5" or 2" at 100 yards, either you, the rifle, the ammo or a combination thereof is doing something wrong.