I'm not doing fancy AI stuff but I have worked a lot with my own bespoke supercollider system where I record whole fretboards of guitars and then play alternative notes based off of certain rules. For whatever dumb reason though, the most natural sounding thing is really just playing, e.g., any random D4 from its possibilities at any given moment.

Timbral differences also exist depending on force, the manner plucked, the already ringing overtones... It's hard to know what you want, but the most natural thing is always going to be some organic variation in the notes in general.

If you have a good ear, you aren't, I don't think, hearing so much the timbral diff in the individual open or fretted notes as much as the fact that a barre chord and an open chord is a different voicing of the same harmony.