Wow. Facinating story. Not a clue what might be causing your imbalance. What are scientific measurements anyway?
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I had this one time and it ended up being a room problem. My left speaker was always lower in volume. I did the swap thing and it went away except now the imaging wasn't right. I even had my ears tested!
I came to the conclusion, when I swapped things, it caused the signal to be dispersed differently eliminating the problem by somehow taking the room out of the picture. (Using one of the new receiver audio setups (Denon 4808ci) it too had shown the left channel down about 3 db and out of phase.)
I finally played around with acoustic treatments and speaker positioning until I got it very close. (Now it still happens from time to time but it is the disc to blame. It's surprising how imbalanced some discs are.)