HomeKit "Apple TV not responding"

I had a 4th Gen Apple TV setup as my HomeKit hub and was working fine. Lately I've noticed the Home App on iPod/iPhone says "Apple TV not responding". I've done all the tier-one support obvious things: Updated iOS and tvOS, cycled power on and off, signed out/in on Apple TV cloud login, etc.

About at wits end, the Apple TV hub seems to be necessary for any newly added devices to show up on other home users (that I invited) iPhones. There will be unrest among the natives soon if I can't make this work.

Quick summary: log in to https://appleid.apple.com/ and change your Apple Id from @me.com to @icloud.com

I recently had the same issue (including homekit invites getting stuck as described in this issue HomeKit invitation stuck). Yesterday I was finally able to resolve this problem after having tried all the obvious things as well (resetting devices, logging out/in of iCloud etc).

Turns out the root cause was some kind of conflict between my Apple Id and iMessage. After taking the following steps everything started working properly again:

1. Change my Apple Id from @me.com to @icloud.com. You can do this by logging in to https://appleid.apple.com/
2. Delete my home from the home app on all devices (including family).
3. Log out of iCloud on all my devices.
4. Log back into iCloud on my iPhone.
5. Create a new home and add my homekit accessoiries.
6. Log back into iCloud on my Apple TV.
7. Invite my family to the home.