need circuit help with headphone amplifier 'thump' and other issues
I am not familiar with your exact situation, but it seems to be related to the fact that one side of your headphone is grounded, while the amplifier output floats at some potential different from ground.

Therefore, consider using an output transformer to isolate the DC floating voltage of the amplifier from the grounded output circuit.  

If you really want to educate and empower yourself, consider building your own transformer.  It is not as hard as the big boyz make it sound.

Back in the day, we used vacuum tube amplifiers.  They used high voltage.  It was possible to save money on a transformer by wiring the headphone between the vacuum tube and the high voltage supply.   As a California board-registered EE, there are some forms of death that are professionally embarrassing for us, so do as I teach you, not as I did when I was young and smart.