From past posts I remember you use Sonarworks to EQ your Clears for studio use. Frankly, I think what you’re saying about them not being as timbrally accurate as stock is due to the SW profile, not any fundamental conflict between accurate tuning and accurate timbre.
A) Sonarworks profiles are made to match their house conception of what a flat sound is. B) Sonarworks profiles for a given model headphone are a compromise between the differing tunings of multiple units of the same model headphone. I’ve seen posts from Sonarworks showing graphs of just how much variance they have to deal with. And that means just how likely it is that any such profile will be accurate for your particular Clear (Pro) headphone.