Hi JeshuaH,
This works for me mostly as well. It was a bit finicky to get it right the first time. It took me several attempts to get it to work.
They key is to watch iTunes on your Mac. When the sound drops and the triangle goes orange. Click the play/pause button on the remote as quickly as possible. The triangle should now become blue again almost immediately. (If it stay orange then rather disconnect and reconnect from the speaker setup in iTunes and wait for it to drop again.) Then once you could get the triangle to turn blue from orange using the ATV remote, it seems you have to click the play/pause button on the AppleTV remote two more times to get the iTunes play button to change from play to pause. Then after a few seconds it should start playing again. (So three clicks of the play/pause button on the ATV remote in total was what worked for me.)
It still drops the connection to the Apple TV4 but only seems to happen when you click on the (blue) triangle to change the speaker setup. Even if you do not change anything, the connection to the Apple TV drops soon thereafter.
So sure looks like a bug as I also airplay to my Marantz in a different room and it keeps playing perfectly with no dropped connections during all of this. It only seems to be the AppleTV that kept on dropping the connection, unless you perform your AppleTV remote trick.
Thanks again, it is a workable work-around until they can pin-point and fix the bug.
Regards
Paul
My setup: MBPr 2015 (Sierra v10.12.3) on WiFi, playing iTunes (v12.6.0.100) and airplay to Apple TV4 (10.1.1) on cat-6 Ethernet Connection and Marantz MCR611 on cat-6 Ethernet connection. My network uses a D-Link ADSL router and a Tenda 24-port Gigabit Ethernet Switch.