Will definitely check out AirParrot 2 for Mac OS X. Seems like a real upgrade over AirPlay.
Worked this out yesterday:
1. Used "Configurator" to reinstall a fresh version the ATV3 software and found the following works. This could be a headache for a lot of schools. We have 20+ Apple TV devices at ours and mounted all over rooms. But!...
2. iOS 9.x = devices will now connect and function normally with AirPlay after the Apple TV onscreen password is entered. Takes around 5 to 10 seconds to connect initially. Entered the onscreen passcode from the AppleTV onto the iOS device. After that it's as smooth as butter. Finally...
3. iOS 8.4.1 = no on screen password required and mirroring via AirPlay is wonderfully fast.
4. OS X El Capitan 10.11.1 = nothing.
5. OS X 10.10 and previous versions totally work great.