How to Solve High-Frequency Suckout in Room?

Thanks all for the info.  I found this great video discussing narrow vs wide dispersion speakers and it covers some of the principles that we’ve discussed here.  
 

Wide vs Narrow Dispersion

I should have been clearer, but when I s said “higher frequencies”, I actually mean upper mids as well.  You can notice that upper part of vocals is toned down on the right, which is annoying.  I tried putting thick moving blankets along the left on that island half-wall, and it did actually help even out the left and right.  But, I don’t really like all the missing higher frequencies with this approach! 
 

So, I’ve concluded that rather than create a balanced suck out on the left, I need to increase the higher frequencies on the right.

I still need to try @milpai ’s idea and block off the gap on the right of my right speakers.  But I think I’d need to use a non absorbing material to preserve the higher frequencies and have them reflect toward the listening position from the right.

When you're doing excessive toe you're doing, time intensity trading, like they talk about in video. You could give it a try as it will move the reflection to the side wall on the right. 

Okay, so I spent half my Saturday totally tearing apart my living room, removing the couch, and bringing in large cushions, moving blankets, and cardboard (my speaker boxes), to play with various configurations.  I also tried the "excessive toe-in" configuration where you have the tweeter's line of fire cross over a few feet in front of the listening position.  I tried moving my entire system extremely to the left.  I also removed my old speakers from the area.

While some things helped a bit (the thing that helped the most was moving the entire system to the left), the issue ALWAYS remained, no matter what I did.  I even tried changing the right speaker so that it was asymmetrically positioned to the left speaker.  I also compared the same tracks with a decent ($500 Sony WH1000 which are great) pair of headphones just to make sure I wasn't imagining things.  Headphones reminded me of what a perfect stereo image is supposed to be.

So, after all that I realized I had accomplished two things: 1) I don't think my room is to blame, and 2) I found I had a ton of crud under my couch which I cleaned up.

Finally, I went back to wondering about my amp.  I swapped the speaker cables on the amp end only - moving the right cable to the left amp terminal and the left cable to the right amp terminal.  And this time, I REALLY listened.  I realized that the problem did in fact move to the left side, from the right!

With this in mind, I now suspect my Gryphon Diablo 300 amp has an issue.  I'm using the internal Gryphon DAC module, so it's possible that is the culprit and not the amp. 

Has anyone heard of something like this happening with an amp before?  What could cause it?  Frustrating as I adore the sound my system is producing other than the lack of stereo image.  On the other hand, I feel like I'm getting closer, in that I'm getting closer to isolating the cause of my issue.

On a related front:  Why sort of meter should I consider investing in to measure the frequency response of my channels?  And what test track should I use for measurement, to prove beyond a doubt it's not in the source material? If I go back to my retailer/Gryphon with this issue, I feel it would be good to be armed with some "proof".

OP,

Thanks for the photos… I like the one with your significant other (?) peering out> Nice system. 
 

With what you have done, I would also would be at wits end. Happily it sounds like you are working to root cause… that it is it is a component problem. That makes sense. Because, yes, as you say room treatments can dial things in… this problem doesn’t seem to be a room problem.