This will be a challenge for me after we move so I’ve been thinking on it.
Has anyone considered or actually done the following? Make, or purchase, a light weight diffuser panel, large enough to “acoustically hide” the TV completely. Hang it from the ceiling, so it’s flat on the ceiling when watching TV, where it’s out of the way and works to minimise ceiling reflections. Lower it by some ingenious mechanism that hinges directly above the face of the TV, so it hangs right in front of the TV.
I’ve not yet got a solution for the mechanism that is aesthetically acceptable and functions well, but I’m sure it’s possible.