You could try some bone conducting head phones. I've been wearing the Shokz brand OpenRun headband all day at work for about 5 months now and it's comfy. I use them in bed sometimes but don't fall asleep in them. They have some new wrap around ear ones that might be comfier to sleep in.
Edit: A full charge will last all day and they recharge quickly.
I've used the Shokz bone conducting headphones and love them. Not sure if OP can find a model that they can sleep in, but the principle is sound. I got mine because I wanted to be able to listen to music without waking up the baby.