For the BIg, Big game you describe, large bore guns, beginning with the .54, then going on up with the .58( 24 gauge), .62( 20 Gauge), .66( 16 ga.) .69( 14 gauge) .73( 12 gauge), .75(10 gauge), and then the larger smooth bores, in 8 ga., 6 ga., 4 ga. and 2 ga. were used. All shots tended to be taken at 50 yards and less. in some cases, the lead was an alloy, like our "wheelweight" to give the ball a greater hardness than a pure lead ball. The idea was to make the ball harder for deeper penetration on Rhino, and Elephant, and Hippo.
All are very large animals, with thick hides. The only animal in N. America that approaches this size of animal would be the Moose, but it has relatively thin skin, and a large bore Rifle, shooting a pure lead ball of at least 3/4 oz. is going to put any moose down with a solid hit to the chest. If you read thru past posts on this forum, you will find that RBs have proven totally effective for taking large bears, moose, and caribou, provided you get close enough. Pass thru shots are the norm, even on these animals, with a few hunters reporting finding a flattened slug under the off-side hide on large bears, occasionally.
The advantages of these large bore MLers are: that they leave a huge entrance wound that lets out a lot of blood; you can use powder charges that don't dislocate your shoulder, but still put enough energy in that large ball to get deep penetration of the vital organs; and the guns will allow you to shoot at game out to 100 yards, about as far as you want to be with open sights, and the trajectory of any RB.
Do penetration testing to give you the confidence in your rifle before you go into the field. You will be surprised at how deep these large balls will penetrate any test medium you use. Then study the animals you intend to hunt to get an idea of the actual size of their chest cavities. Visit a zoo and observe the animals as close as you can get. :hatsoff: