No, no “poking fun” intended. This is scientific discourse. If in the northern hemisphere shooting south, as you say, the target is moving east faster than the rifle. however, the rifle’s muzzle is moving east faster than its chamber. Therefore it seems that the barrel movement would offset any need for aim compensation.
Its a bit harder, even for me, to try to analyze the what may be occurring in the internal ballistics compared to once the bullet has left the barrel and is its own entity.
I suspect it doesn’t matter that the muzzle is traveling at some infinitely smaller amount faster than the chamber. The southern target is still traveling east faster than the muzzle at the moment the bullet exits, so there is still an uncompensated difference in eastward velocity between exit and impact points.