Cannot connect iMac display to Apple TV
I want to see my iMac (OS X 10.10.5) desktop via AirDisplay on Apple TV. If I click the AirDisplay icon in the Mac's menu bar, I see my Apple TV listed. But if I select it there, I get a spinning wheel and then a pop-up windows "Could not connect to "[name of Apple TV]" (actual name redacted here).
Likewise, with my iMac's iTunes Home Sharing enabled and with iTunes running, if on the Apple TV I go to the Computers app it tries to load my iTunes Library but eventually says it cannot connect.
This happens even with Intego Net Barrier disabled and even with the OS X application firewall disabled.
iMac is hard-wired (via Ethernet) to Apple AirPort Extreme version 7.7.3 router; Apple TV is connected via Wi-fi to the same LAN, of course.
AirPlay is enabled on the Apple TV, and there are no Access Control settings on, and "Require Device Verification" is set to Off.
All current updates to Apple TV have been installed.
I can see the usual Apple TV apps, etc., when my TV is connected to Apple TV. (Thus the Apple TV is on the LAN.)
I've tried rebooting the Apple TV, my iMac, and the AirPort Extreme, all to no avail.
If on my iMac I run Bonjour Browser.app, among the local services listed I do see my Apple TV listed and with an IP address that in the OS X Terminal I can successfully ping!
Oddly, a different iMac on the same LAN via Wi-fi can connect to the Apple TV so that its desktop displays via AirDisplay.
Any ideas how to proceed?
iMac, OS X Yosemite (10.10.5), 3.4GHz Corei7, 16GB, SSD + 2T HD