OK, so I did a bit more searching using different keywords, and I found the solution, which of course is frustratingly obvious. My headphones have a mic, and so have three bands on the audio jack - it’s obviously causing some major phasing issues, because I dug out an old set (the only set I hadn’t tried, and the only set without a mic), and with just the 2 bands on the jack, they work fine.
So, all the hours of frustration come down to that 
At least I get a new pair of headphones out of it I guess… Thanks again for all of your help, hopefully my next contribution to this forum is a little more useful.