I am not an expert. I did happen to see a nice comparison of the .375 H&H to .375 Weatherby, .375 Remington Ultra Mag, and the .378 Weatherby. It is in Guns & Ammo, September 2004. I quote Mr. Craig Boddington "The .378 develops well over 100 ft-lbs of recoil-about twice that of the .375 H&H. And it's a sharper recoil." With 300 grain bullets the velocity gain is almost 400 fps, and at 400 yards it remains 300 fps faster. "With more than 5700 ft-lbs, the .378 is, of course, on a different plane. Energywise the Weatherby round is in the class of the .458 Lott and the .500 Nitro Express."
I wonder if the Ruger can take the punishment. If the Ruger is available in the .458 Lott, perhaps it is strong enough.
Because you actually have the rounds in your garage, I know you can!
I believe the factory ammo sells for $100 per box now. You could auction it off, I suppose, and get a nice Handi-Rifle?