> Given this, I think it's reasonable to select the venerable 7.62x39. This is a common chambering for semi-automatic and even automatic rifles with high-capacity magazines, which would obviate the need to load each bullet individually. It also is easy to obtain armor-piercing rounds in this caliber if penetration is your concern. This is still a punishing round to fire a lot of, but with a modern recoil management system it's manageable.
So, the .308 is extremely common in the US and is somewhat similar to the 7.62x39. A .308 fires a typical round with, oh about 2500 ft-lbs of muzzle energy. Meanwhile a 44mag has maybe 1000 ft-lbs of muzzle energy. An Ak-47 is also 7.62x39 and has ~ 1500 ft-lbs of energy. That's a hell of a lot more grunt than a 44 magnum, any way you dice it.
At that point, skip the armor-piercing or FMJ and go hollow point. There's more than enough power in that round and the larger wound channel is probably a plus.