Flat screen between speakers, again.

two thoughts ,
sound absorbing curtains that cover tv when not it use.
or sound absorbing panels by I think ATS makes a clip that mounts to back of panel and the female part mounts to Wall and slides down into it . make a lightweight backer to push panel off wall whatever the tv is 4"? and mount that to panel grab the panels 24 x36 or 48 " or custom and side them down into slots and they would hang in front of tv covering it .( they may flex a little because they would be hanging but done right they would be fine . I use the panels in my dedicated room , if you pm me I can send you a pick and a scribble of what im saying 

My neighbor had a carpenter fit a cabinet to his high ceiling with a motorized carriage that takes the tv into the cabinet when not in use.  

Dependent on the speaker type (dipole etc.) and the rest of the room.As usual the answer is unknown until you try.

Sure, but heavy curtains work fine too. While shopping, put your ear up to them, and you’ll hear the better one’s.

Also, push the panel as far back as you can. If there’s any room behind it, like say 6" or more, you would not be wrong to treat that space with a thick panel.

Also, consider the floor between behind the speakers. I find high frequency hash lives there for some reason. If you want to experiment by throwing some blankets or pillows over the TV, and on the floor you’ll gain first hand knowledge inexpensively about your potential benefits and rewards.

Take a dowel rod, or even a 2X2 board about the width of the TV. Drape a comforter or thick blanket over the dowel. Drop the dowel over the top edge of the TV so the comforter covers the TV. If you like the results, tidy it up and make it a permanent device to use when listening, or just know that a more permanent solution would be worth your efforts.