You're asking the wrong guy 🙂
But here is what I think: There is no way to get the ATV to keep outputting if it believes the "TV" is off or disconnected. So the trick would be to make the ATV believe there is an active TV connected to it. Maybe some TVs can have their HDMI input active with audio out but no TV display, I don't know?
Or it could probably be done with an intelligent HDMI device (not one that defers to the TV for all the HDMI signalling).Maybe one of the newer sound systems with HDMI input/output could do it. It has to be an intelligent device that "acts" like a TV (and I don't know exactly in which way: probably HDCP related), from which you take the audio.
On the other hand, maybe they'll change some settings in a future update and that will be made easier, but I doubt it, I think it is a Copyright "safety" feature to keep the Copyright's holders off their back.
Obviously there are many other ways to get your music out with the TV off if you get the Apple TV out of the loop, but that is not a discussion for this post 😉