Hi,
Which Apple TV do you currently have?
So just to clarify, you run the HDMI from the Apple TV into the AV Receiver and then the output of this into the TV? Is there anything that is being sent from the TV to the receiver such as HDMI ARC or similar?
Could you try unplugging the connection between the TV and the AV Receiver and tell me the result? It sounds like signal is somehow being sent through the TV for something and when the TV is turned off, this is dramatically slowing the signal chain?
Let me know.
A.