I'm not immediately convinced that "effectively changing the shape" is a coherent idea. The lift effect either crucially depends on the actual, unchanging shape of the aerofoil or it doesn't. Flying upside-down proves that it doesn't. Maybe all we're disproving is a straw-man of a "Bernoulli-ist" position, but we're disproving it all right.
EDIT: trying to think what you might mean by "effectively changing the shape". Do you just mean that an upside-down aerofoil is a reflection of the aerofoil the right way up? Because that's the entire point of the argument you seem to be trying to rebut.
EDIT: trying to think what you might mean by "effectively changing the shape". Do you just mean that an upside-down aerofoil is a reflection of the aerofoil the right way up? Because that's the entire point of the argument you seem to be trying to rebut.