As far as I can see there's no need to re-encrypt the signal - just leave it as a non-HDCP stream?
There are HDMI splitters which silently strip HDCP to output to two screens at once - they don't advertise this feature but they do it anyway in order to function. In order to achieve the overlay you'd just need one of these and then a non-HDCP-aware overlay apparatus before the display.
https://www.reddit.com/r/VIDEOENGINEERING/comments/xme482/hd...