Please mention whether you’re on stable, beta, or a different update channel. There’s a good chance most bugs on the stable update channel have been fixed already, so anyone on the beta update can let people know if the bug they’re facing is already fixed.
What headphones in particular are you using? Because with standard AD2P you’re limited to mSBC at best, but maybe your device has some proprietary implementation.
You could try with a hardware dongle, but no guarantee that will work either.
At least in the long run it should be fixed by Bluetooth LE audio, but I’m not sure if the Deck properly supports it yet, and it requires new audio devices as well.