I like your room as a room, and I do love built ins, but you do face challenges. I think you are best off trying to get things in order with the equipment you have first, then thinking about new speakers.
You will be getting lots of side first reflections from the right and not many from the left. Ideally you have balance of direct sound and first reflections on each side. That's the main issue.
I can see options that I might try. Simple: add a panel outside the Left speaker, to get MORE first reflections and try to balance the sound from both speakers. I think this might work if you can move the seating back, so the back of the couch is lined up with the green on its right side. But I am not sure if you can make that work and leave space to get to the seating comfortably.
Treating the right side to kill more reflections would be tough.
Complicated: corner placement, which would not look as good architecturally and leaves you with needing to figure out how to place the screen in the corner. Corner placements can work, but a lot depends on the entire room and making sure it works for all the things you use it for. Corner placements eat up more space, that's for sure. The fixed cables would make this hard.
Things to do electronically: Different levels on the speakers might help a bit, good old "balance" settings if you have them. Or you could measure, and EQ the two speakers separately, which would help. This would be my first go to, btw.
Getting a calibrated mike and downloading REW will be a HUGE help. Even a phone SPL meter, play white noise from YouTube through each speaker individually, look for left and right levels differences... that will tell you something of what you face. If nothing else you would know that the right side is +Xdb higher.
I am a big fan of the tools in wiim streamer now. 10 band eq, separate L/R eq, room correction if you have an Iphone, and a good streaming interface. This might be an inexpensive way to get some tools, particularly if you don't have a streamer now.
