Flat screen between speakers, again.

Perhaps a 5 sided box with absorption on one side and diffusion on the other side that could slip over the tv might work? Just be mindful of the cabling.

Perhaps a 5 sided box with absorption on one side and diffusion on the other side that could slip over the tv might work? The inside could be lined with microfiber. Just be mindful of the cabling.

Long ago way before the projection screen that mounts on the wall I had a TV. I mean a real vacuum tube TV. As thick as it was wide, which wasn't much, only 32" screen. Yet that was big enough to hear the improvement when covered with a thick blanket. Forget towel, THICK blanket. Think quilt.  

Forget diffuser, too heavy, cumbersome and expensive. What you want is absorption. A nice cheap and light, easy to move around panel.  

The stuff you want is called Owens Corning 703 acoustic panel. I would just get one, 1" thick will be plenty, and wrap it in some open weave (think speaker dust cover) fabric. 

Make something to hang it over the screen when listening, put it on top of the TV when watching. Easy peasy.

Diffusion ... tuned to a limited range ... to be determined ... 

Thanks for everyone's responses. What I should add is that this is only one aspect of my diving into "room treatment". Whatever the final solution ends up being, I do think I would prefer exploring an actual room treatment option, as opposed to throwing a blanket over it.Now that the good weather is disappearing and I am not spending 4 or 5 days a week at the golf course, perhaps I will finally get off my butt and get things fixed. One Covid byproduct is more time on my hands.