The interesting aspect to me here is how one would get a clean finish on the inside face of the cruck's curve.
And also, I am one of those who works with both a left hand and a right hand broad axe. The terms are somewhat misleading, as a left hand axe does not require one to use his left hand to use it. It just notes where you stand in reference to the timber. In fact, I almost prefer to use a 'left hand' axe.