Exactly. The 432Hz frequency is also associated with the so-called solfeggio scale, yet doesn't appear in it. Then there are the countless references to the Schumann resonances, again - no 432Hz there either. But it "sounds like it could be kinda related somehow", so there are tons of Youtube videos and stuff that try to draw parallels.
As Bea pointed out there's a low eigenmode frequency as anticipated, nothing unexpected there.
String tension is reduced in applicable instruments which alters the voicing a little, etc. You're right though; the fundamental flaw of trying to apply these notions to music is that playing a A tuned to 432Hz or 440Hz will yield a peak encompassing *both* frequencies strongly due to the Q of the note, so to speak.
Well... today we have fairly clean pitch alteration capabilities without tempo changes so one could record a harmonica (or other untunable instrument) and adjust it post-rec to match the rest of the piece. Anything sampled should be easy to do. I've actually detuned a synth with a piano patch to play along to some stuff (Beatles, for example). They recorded at concert pitch, I'm sure, but the tape was sped up or slowed down. An example of an actually detuned piano would be Coldplay's The Scientist, which sits at - IIRC - 441.3Hz.