Sending Network Stream from Playlist (.m3u8) to AirPlay?
Well as you said with AirParrot (which btw is also great for Windows users) you can extend your display to a "Specific App…" thus QuickTime/VLC/MplayerX. To avoid choppy video you should use Ethernet cable…
I don't know what can be done and how Mavericks reacts with the second display feature while changing desktop… But I believe you have the same kind of lags.

Air Video HD allows from local device to AppleTV streams : http://www.inmethod.com/airvideohd/index.html
It should not be to complicated to route your favorite remote server on a local IP address /etc/hosts or something like that …

The alternative that would work for AppleTV v2 and v3 (that last one not being jail braked) is to emulate the "Trailers" service to be able to stream from "PlexConnect" :
— http://gigaom.com/2013/06/04/plex-apple-tv-plexconnect/
— http://www.youtube.com/watch?v=H1s09hRaWm4