pulseaudio – Switch/invert left and right audio channels on Linux system-wide

The situation

Sometimes,

• I have my stereo speakers behind me, or
• I wear my headphones with left and right ear inverted for physical comfort reasons.

My question

How can I invert the left and right audio channels easily on Linux?

The ideal solution would be system wide and easy to setup and revert (for when I’m not in the headphones or speaker situation anymore), without interruption of the playing audio stream.

A limited solution

I use the pan audio filter from the ffmpeg project when playing a media with mpv (pan="stereo|FL=FR|FR=FL") but it only applies to this particular media within mpv…

Environment

I have PulseAudio and Alsa.