I have a Chapuis in 9,3x74R. It has become my favorite hunting rifle under 40 cal. [I have 2 British big bore doubles]. I have taken several animals with this rifle including big pigs, black bear, and several African Plains game. It weighs 7 1/4 lbs without the scope, I have two scopes fitted and sighted in in QD mounts. I just cannot say enough nice things about this rifle.
I would still like to have a 375 H&H rifle to test the theory. A 375 double with scope in QD mounts [that works] would be an excellent double for the American hunter. [You just cannot find factroy 9,3 ammo many places].
Several AR members have 375 H&H doubles and none have mentioned any problems.
I know a fella that has several FINE British double rifles. He told me his favorite double rifle to hunt with was his Heym 458 Win Mag, with scope in which he shoots Barnes X bullets. [Thus breaking every double rifle rule].
I have seen him shoots this double and it shoots plenty good at 100 yards for sure.
I say go for it.
If you are looking at a 375 double take a look at the Chapuis.