BIFL and Bluetooth are typically an impossible combo because Bluetooth means more batteries and electronics to break/be unreplaceable. Maybe modular systems will come in the future but they'd need to use a completely generic set of batteries.
My best suggestion, based on what you describe as your problem with wired headphones, is to get headphones with a removable cable, as those cables are generally pretty standard. I know sennheiser had a lock in mechanism but you can get third party cables. Also, I was able to take that out of my HD599s and use the headphones with a Bose cable.