Hi dragon49,
First of, congrats on finding a working solution!
Before responding to your questions: I’m not an electrical engineer and my answer’s based on my high school and general understanding.
From what I understand the original amp design doesn’t have ‘true’ ground. Therefore, the plus and minus are relative to eachother, thus giving opportunity to pick up hum. Apparently, switching on the blue tooth is ‘equalising’ the plus and minus to a level equal to when having true ground.
Probably, you have been researching yourself. Anyway, when trying to understand the common cause of hum, I did some investigating and stumbled upon this link: https://www.psaudio.com/ps-how/how-to-find-and-fix-hum/ from which I comprehend you have reached a similar solution as with the AC Chester plug.
This link I also found helpful understanding: https://www.techwalla.com/articles/how-to-eliminate-amplifier-hum-from-speakers. I don’t quite understand what you did when applying the three pong connector. What did you connect the ground prong with? It seems that you created true ground by using the ‘main output of power negative’ and connecting it to ground with a separate wire, although I don’t really understand what this does electrically. It also seems you might combine this solution with your first three wire grounding plug connection.
In the above some relevant information might be missing for full understanding.
I hope this helps providing further understanding, but please do fill in where our common understanding of the schematic can be further augmented and ask anything to further deep dive into the matter.