Kind of funny that I have both the 350 RemMag and 405 Win Barrels.
My experience with the 405 is limited. I took it to the range and with a reciever sight on back I needed a taller front sight as the Hornady Factory Ammo was printing about 4" high at 50 yds with said reciever sight bottomed out. T/C was quick to send out, free of charge I might add, 2 taller front sights. Expirimentation has been stalled by hunting season but I really can't imagine that a round that T.R. used for Lion and Rhino (though the latter would probably be a poor choice with the Hornady Factory load) could not kill any kind of a wild Boar. Bullet selection is kind of thin in 405 unless you take into account all of the .41 pistol bullets both cast and jacketed, plus cast bullets from a wide assortment of makers in 300 and 400 gr weights made for the 405 Win and other .40 Caliber rifles from the late 1800's.
Obviously if you are concerned with sectional densities then a 300 gr .411 Dia bullet has a higher SD than a 300 gr .458 dia bullet. Both can be started about the same speed from the respective cartridges and I would bet the .405 would penetrate deeper though either will do the job.
A .375 H&H barrel has been on my list though it keeps getting shoved back. It would definitely be fun to play with though I can't really imagine needing that much horsepower for anything I hunt (same holds true for the .405 as well but it just has that certain flavor to it). If I were to ever go to Africa (I really don't see it happening but...) I would be more apt to take a couple Bolt Guns rather than any single shot.
The great thing about the Encore and the Factory and CUstom Chamberings available is that you can try just about any round you want and say you have been there done that. Sean