RG this is how confusing it is for me. What you have just said as I read and understand it. You cannot file a consistent angled bevel on the ax without ruining its overall geometry.
I see forum axes all the time with a swell, and a even width bevel (or approximately even width. ) Maybe i need the Ax Book and get up to speed, as it is with my current level of understanding, the width of the bevel, and the radius of the edge are the two main factors controlling the depth of cut w/o binding. Throwing a chip being largely governed by the relationship of one cut to the previous cut, the nature of the wood along with the angles of those cuts.
The swell is putting meat behind the edge and inertia in the most beneficial area, driving the edge deeper. Extra metal on the perimeters of the head as in a true wedge is not really helping as much. Being evenly distributed as it is; it is mass, true. With a swel,l that same equivalent mass is focused to a more direct effect.
That may be completely wrong. I dont need to be right but I would like to understand axe geometry.
hollowing and reprofiling the cheeks seems to have nothing to do with chopping felling of notching. Unless y'alls axes are cutting that deep 1/2 way up the bit