As to Peter, while I suspect that some of his weird chords were developed by experiment rather than theory, I'm pretty sure he used them with a lot of discrimination.

Absolutely. 'Happy accident' wasn't meant to suggest that he stumbled on those chords on the morning of the recording session - I know that PB listened hard to what he was doing, & played what he played because it worked.

I usually leave out the thirds when chording on a concertina

That's really interesting. Perhaps it's because most of the triads are so easy on an EC, but it had never occurred to me to do this.