Well, I think you've elucidated some interesting stuff here; I've looked at motorcycle throttle cable linkages and stuff for forty years without really getting it; or thinking much about it, butterfly valves are basically ____ from a control standpoint with the possible exception of multiple opposed blade types in mixing applications; yet one particular manufacturer of equipment that I work on uses them on gas fired equipment exceeding 1,300,000 up to at least 5,600,000 btuh, and these are burners with 15:1 turn down.
Controllable / repeatable [predictable] air flow across a butterfly valve occurs across a narrow portion of the full gradiant; but to plot those values [that you've given so far] on a graph, would approximate the characteristics of an equal percentage valve.
How you arrive at the cross-sectional area of the resultant crescent at each butterfly position is interesting as well, in any event, the bypass [4mm or whatever it is] cross sectional area does not work in a similar orifice plate way that the throttle plate does; and cannot be imagined solely on the basis of relative cross sectional area to provide proportionate flow, It has length that translates into resistance that is [roughly] proportional to the square of velocity, so there's all of that,