Asymmetric Room

For a control, select a vocal cut that should be well-recorded recently - but seems to have distortion.*   Then proceed with many experiments to locate the cause of the distortion.  (This can take several days.)

A few suggestions: (1) throw a wool blanket over the coffee table in front of the listening position (2) unplug any HT gear - leaving only 2 channel powered (3)  make sure that power cords aren’t touching or paralleling any signal cables (4) confirm that all cable connectors are firmly plugged in - including AC plugs (5) mark the speaker positions with tape, then radically change their location - not just the toe-in (6) any other experiments. 

Good luck!

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* Years ago, when I had a similar issue, I selected Patty Griffin’s song, ’Let Him Fly’.   Some of her high notes were painful to my ears.  Now, they’re smooth as silk.   

In my case, the solution was clean power - with special attention to the streaming head end - modem/router/access point.  YMMV

"Any elegant solutions for covering the TV, I am all ears."

Quilt.

As @knock1 mentioned, a quilt will help with the TV reflection. You can buy a 1" dowel rod and cut it to the width of your TV. Drape 5-6" over the dowel and tack or sew it. When you want to listen to music, slip the quilt covered dowel over the top edge of the TV so the quilt is covering the TV. When you want to watch TV, lift it out and drop it below. Works really well...

@steakster Listening within 1foot of the speakers revealed the room while it may not be helping, is not the cause of my problem as the distortion remained the same. Your recommendations are well founded. I did try covering my coffee table. Thanks 

@reubent  @knock1 While not my current problem, will implement the dowel quilt solution. Thanks 

@OP While not necessarily the cause of your problem, you will get comb filtering from reflections from your sofa as well. So a throw on it will help as well. If you are hearing the problem within a foot of the speaker, check that it's not a resonance in the speaker itself - check that all the drive units are properly torqued.