Hmmmm... Seems like I have somewhat of a reputation going here as a person that likes more gun than is necessary - but always enough to get the job done.
With all that being said, my own personal arsenal consists of a .62 caliber English Sporting Rifle, a .69 caliber English Sporting Rifle and an eight bore double rifle.
The .62 is my "plinking" rifle, which I would use for casual shooting, target matches and maybe deer hunting. For plinking/targets, I use 135 grains of Ffg. For more serious, I up it to 200 grains Ffg.
The .69 is my elk rifle. For shooting, I run about 165 grains Ffg, for serious, 200 grains Ffg.
The 8 bore was built with Africa in mind, although that hasn't happened yet, and at this point, I am doubtful if it will. The gun did go to Africa, but I didn't be the one to take it. That fellow shot a 525 pound male lion with it. He said the ball went in high at the chest, went the entire lenght of his torso, smashed the pelvic girdle, and kept on going out its butt. Flipped him in the air and did a turn and a half, wound up on his back, facing the oposite direction. Penetration? I'd say. Power? Plenty to spare.
I had a beautiful .72 caliber that I dropped a bison with, but sold it to a good friend. Strangely enough, that rifle was probably the best shooting of the bunch.
I really like a slow twist on the big bores, .62 through .72 had 1:104, wide lands, narrow grooves, and shallow rifling. The all shoot 200 to 225 grains of Ffg well. The 8 bore has 1:144 and seems to like 300 grians of Fg.
I think any of the above calibers would look good in a Jaeger style rifle. The .62 would want to be minimum 1 1/8 at the breech and the .69 and the .72 would be 1 1/4". I don't think I would go with any bigger bore.
With a 200 grain charge of Ffg in the .62 with a 32" barrel, I am getting about 2,000 fps. The .72 with 200 grains (might have been 225) gave around 1,800 fps. That was good enough to knock an 1,800 pound bison off his feet and roll him onto his back at 100 yards. He was shot in the neck, the ball clipped his spine and came to rest under the hide on the far side. I'd say that is adequate penetration.
I don't know of anything else I can add to this. You might try Beartooth Bullets website and play with some of their ballistic calculators to see the difference between your current rifle and some of the big bores. Quite a difference.
Let us know what you wind up thinking about.