Mike:
What Phil said. I'll add that the way a beavertail is usually used only exacerbates the weight issue.
The fore-end is not a handle. A double rifle should be fired with the leading hand grasping the barrels, not the fore-end, with the fingers wrapped around the topside enough to ensure that the barrels do not kick out of the hand. The extra girth of a beavertail makes the correct grip more difficult. When the beavertail is grasped in the usual manner that protects the fingers from hot steel, the result is that the leading hand is pulling down on the fore-end at the same time that the barrels jerk skyward in the recoil arc. The extra stress that this, plus the extra weight, puts on the lug makes failure more likely.
I'm not suggesting that this failure is common, but it does happen. If it happens with a 12 bore game gun, who cares? With a double rifle that will be used on dangerous game, you want failsafe reliability and try to eliminate the things that can fail at the worst time and in the worst place. You might be fine at .375 recoil levels, but I wouldn't set it up that way. While it's true that quite a number of current makers offer beavertails on large caliber double rifles, keep in mind that they do so because that's what the comsumers want, not because it's a good idea.
My .400/.360 Purdey has one standing leaf for 100, and two folding for 200 and 300. I've always found this perfect. I shoot smaller groups blindfolded than I do with a ghost ring, so I can't help you there.
The recommendation for the 9.3X74R is usually a good one. The difference between it and the .375 Flanged Magnum isn't much, and ammunition and components are a lot easier to find. However, the .375 is a slightly lower pressure round than the 9.3, and being a Holland caliber, it will have substantially better resale than the same rifle in 9.3.
The Holland posted in the link has reversed triggers, a rolled left edge guard, and was originally stocked with cast on. It is an original left handed gun. Yeah, the top lever operates in the usual direction. Lots of lefties are accustomed to using right handed doubles, are used to the usual right-swinging top lever, and don't want it reversed.
