I would think .30-06.
The range is pretty close on those helicopter hunts (there are videos showing 12 gauge shotguns with buckshot loads being used); a .300 Blackout has more than adequate thump. I think I’d stick with .223, though I’d use a good sporting load with an expanding bullet. You definitely want a rifle/cartridge combo that allows a decent magazine size. You don’t get that much time aloft; better to be shooting than loading.
I would think .30-06.>>>>>>>>>>>>>
You know, chosing a caiber is like choosing two pairs of shoes.One for yourself and one for the target. The one caliber has to fit both the shooter and the target.
There is a lot of variation in reference. For this reason there is no best caliber. Although it was against the law 50 years ago, I saw a native Canadian shoot a moose with a .22 cal. short, single shot trapping rifle. It was a side on shot at about 70 yards with the moose in the water up to his shoulders, a full racked bull.
Dropped him like a sack of potatoes, hit him right in the ear canal and went right to the brain. It was dead before it fell.
Ever since then I don’t tell anyone but myself what caliber should be used.