I haven't read the thread(s) in the other forum(s) but is there a mention of the kinds of SPL that would correspond to these large capacitance variations?
Another thing that occurs to me is that, at those displacements the validity of Hooke's Law for the diaphragm may also be a significant consideration for any linearity/distortion issues. In this case I would expect the deviation from linearity to be mostly symmetrical about the zero SPL point, slightly offset by the initial displacement due to the electric field, hence leading to mostly odd-order distortion.
One of the problems with measurements of transducers like this one is getting a guaranteed clean test signal to begin with. I wonder if anyone has done something similar to the things Klippel and that other outfit do for loudspeakers, where the pressure on each side of the transducer is changed by an external regulated pump to produce the displacement? Applied to capsules this would not give you the whole story of course, basically operating at "d.c.", and neglecting a whole lot of other details like backwaves/reflections/damping, grill effects, modal breakup, etc., but it could provide some useful data on these basic issues of force, displacement, and displacement-dependent capacitance.
The instrumentation for a capsule could be simpler, probably relying on heights of fluids in a barometer-like arrangement. Safer too....