Speaker Placement Issue/Thoughts

Pretty basic suggestion, but have you used a tape measure to make sure your speakers are equal distance (probably yes). How about sound absorption panels on the side walls-maybe a tapestry or something to help tame side wall reflections? That can help alot when trying to create a solid center image.

Some amps like the TAD Hibachis in my 2 channel a/v system have output level adjustments on-board which can be very effective for providing left/right balance when needed for whatever reason.

Placing speakers to match volume levels is probably not a productive approach as you have found. Placement is key for soundstage, imaging, bass levels etc. Placement to match loudness is likely different than placement to optimize these other areas where placement is the key.

I have a similar issue in my non-symetrical room. My expericnce has shown that it only takes a couple of inches, but I guess that will depend on factors secific to your situation.
As I see it you hae 3 choices:
1. Move the left speaker to the left, thereby moving it farther away from you
2. Move the right speaker to the left, thereby moving it closer to you
3. Move your seat to the right, thereby moving the left speaker farther and the right speaker closer

You could also do a little #1 and a little #2

If you've already tried swapping left/ right inputs to eliminate a mismatch at the source/cabling, try swapping the leads from the amp to speaker- in other words- remove the cable from the left speaker terminals and move them to the right speaker and vice-versa, leaving the connections at the amp end the same.
If your speakers are toed-in at all, try changing the toe-in angle on one speaker only, leaving the distance from the inside-rear corner of the speaker to the back wall the same-in other words:pivot on the inside front spike. See if the image moves. Don't be afraid to try a drastic change to make it obvious.If there's an equipment rack between the speakers check the distance from it's edges to the speaker- this was messing up the center image on my system at one point- making the distance equal took care of it. I put blue painters masking tape on the floor before I make these adjustments so I can always get back to where I was. If all else fails, move the listening chair a bit.

I have lived for years with a similar situation. The balance seems always weighted toward the left side. I tried everything you can try (speaker placement, component replacement, etc.). I have even had my hearing checked and found no difference, right to left. I have now--after years of torture--simply adjusted the balance control (or the volume controls on my Audible Illusions preamp) to establish the true apparent balance and have learned to live calmly with the situation.
It's living comfortably with the skewed balance control that is the hard part.