Told you......audiophile 😊
Kidding aside:
I have a similar issue that has been annoying at times. First thing that comes to mind and what is the problem in my system is...no surprise, the room. Even though the speakers are equidistant from the room corners, the construction of my room is very different where the left speaker is situated vs the right. On the left is a load bearing brick wall with shelves holding a couple thousand lps. On the right, it is not a load bearing wall with a built in cabinet with glass doors and then large pocket doors. Left wall is very dense and the right wall is resonant and reflective. The rear half of the room is essentially the same. The sound is audibly thinner and brighter on the right side of the room; bassier and slightly louder on the left. Result is that center images lean slightly left,
Are there any major differences in the construction of your room left/right; or major differences re furniture or other items in the room left/right? Is the left speaker closer to that corner of the room or the left wall? If it’s any of the above then you can experiment with placement if possible or adding/removing large items in the proximity of the speakers.
However, if the problem is in one of your components:
You say that when you switched output cables on the tunerS that the problem switched sides. This suggests that the problem is a tuner output balance problem. But, ALL your tuners have the same problem? Highly unlikely. Interesting. You also say that your pop cds exhibit the same problem. Even more Interesting because this suggests that the problem is with your amp (integrated?). This is what I would do to trouble shoot:
You have to be VERY methodical every step of the way, First, eliminate the room. Listen with headphones. Do you still have the same problem?
When you switched output cables, I assume you switched only at one end, not both. If you switched the cables at both ends and the problem went to the other side then it’s possible that the problem is one of the cables. I experienced a similar problem once that was the result of a bad solder joint in one of the cables; and another time it was the RCA output jack on a CD player that was about to fail. However, make sure that you listen to more than one recording; some recordings have less than perfect channel balance and can really confuse matters.
Try headphones and get back to us. Several more steps in the process.