How to Solve High-Frequency Suckout in Room?

Thank you for your response and it's always nice to see pictures of the gear in the listening space.  Your gear is miles above mine so please take this with a grain of salt.

I experienced a similar problem as you are having, switched speaker positions and the imbalance (for lack of a better description) stayed on the same side of my room.  And when standing close to the speakers there was no imbalance.  

I have no idea what this means, but in my case I found that if I stand near my listening position and face away from the speakers, the sound was identical from both speakers.  I eventually decided it may be a hearing issue and by adjusting my speaker position I was able to compensate for the difference.

I have been following your last few threads and remember in a prior thread you emphasized you wanted just a TAD more bass but did not want to use digital sound processing to achieve it.  I've never used any DSP so consider this coming from a real amateur.  But seeing your set up, it's hard to see how you will fit RELs in the room without a major reshuffle of your gear and audio furniture and to also take care of the treble problem maybe you should consider it.  A lot of people swear by it.

I am only speculating, but it seems to cure the treble suck out on the right you are going to need to find a way to create an equal suck out on the left without DSP???  Again, just guessing out loud.

The wall is reflecting too much mids from about 1-4 khz, that makes the highs when you listen to that channel alone seem suppressed. Effectively they are in comparison.  You will even get some mids from the left channel reflecting off that close wall too. You need left / right room response measurement to nail it down.

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.