With everything booted up and connected, try a NVPRAM reset, this has helped some people.
Power down mac, leave TV on, power up the mac holding the following keys before the start up chime:
option, command,P,R,(no commas) continue to hold till you hear the start chime 2 times, then release.
If no joy, try a reboot.
Hope this helps
Applecare went through all the usual stuff including kext file removal, launch daemos, etc., and couldn't solve it. They then had me do a Data Capture with the HDMI plugged in and generated all sorts of data which they will send to their engineering department--said it may take a few days. Sounds as though it's a firmware issue but who knows?
Anyway, I would respectfully suggest that anyone else with this problem not spend a lot of time on their own trying to fix it until Apple figures it out, because there is no easy answer, apparently.