Is there maybe a Bluetooth option to send the audio to a Bluetooth headphone?
Oh, I wish. PJRC doesn't have anything like this.
Maybe there are good bluetooth audio to I2S products? I have not personally used any. A couple threads have come up on this forum where people tried to use one, but they board they bought had poor documentation or compatibility problems.
Just to keep things in perspective, this would certainly be "overkill" compared to just using the existing audio shield....