Have you tried to unplug all headphones and then activate bluetooth. It sounds as if the magnetic switch is stuck.

Acoustune do a 4.4 right angled Pentaconn balanced cable (ARK13 I believe). It's a good cable, I used it with a pair of XBA-H3's and now with some Campfire Andromedas. I got mine from Accessory Jack, cheaper than the Sony cable.