Flat screen between speakers, again.

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. 

Tony, I recommended a blanket as an experiment to see what if any sonic change occurs vs. the TV glass.

In my case, I was very satisfied with the sound from my system but wanted to see if eliminating reflections off the TV would be beneficial. I tried absorbion and it changed the imaging. So I tried a light blanket and I heard a more focused 3D image; it's like the TV disappeared. 
Now I use a the cotton blanket cut to size as my treatment.

@lowrider57
What colour blanket? (Just kidding.)
I have a comforter I can try, but I also have several 1' x 4' cheap foam absorption panels that are quite light. Perhaps I can attach them to a thin 4' x 5' panel and hang that on the TV with padded hooks. The only risk is damaging the TV screen, which would really suck.

I have a pair of the GIK free-standing panels, 4' x 2'.  This allows you to experiment with placement.  I started off with the pair cosied together directly in front of the screen and as close to it as possible.  But I ended up with them separated, at 45 degrees to screen, half way between two side edges of screen and back corners of speakers.  Moral of the story: the most obvious place for acoustic treatment may not be the most effective.