Im a lefty and don't do bolt guns. That limits me to autos, pumps, and levers for repeaters. Doubles are too expensive to be practical. So all traditional bolt calibers are out. 375, 416, 458, etc.
I personally think an AR10 pattern rifle in .308 with a 20 round mag and 165 or 180 gr A-Frames would be pretty nasty. Im always wondering why a 10mm pistol is chosen over a rifle like this but.... Now, Im unsure whether a 20 round mag is legal in AK for hunting but I don't remember that stipulation being made by the OP. If this suggestion is a little too "PlayStation" then an 1895 rifle in 45/70 with 405gr hardcasts at a suitable velocity will do.
Other than that I would have to go with a 12ga pump and Brenneke 3" slugs. Green lightning or black magic or whatever the good one is.