In private mode, if bluetooth headphones are used, there is significant audio lag. My suggestion is to add a config for sync audio, something to buffer the video, send the audio and then a few miliseconds after the audio is sent then send the video to screen.
It would be nice to give this option in the mobile application (e.g. below private mode) so the user could set up an optimal buffer. Something like "delay video in X miliseconds". I thing that something between 0 and 2000ms would be enough.