Swap L/R channels with the cables and see if it follows the cable.
I've also seen cases where the depth at which a plug mates to the jack makes a difference, but that's usually a sign of marginal jacks or poor mounting of the jacks/backplate design.
I've also chased this type of problem and found a bad joint in the terminations of interconnects before - visually looked perfect upon inspection, but upon mild flexing of the cable near the termination (while hooked up) it would "bzzzt" - it could have easily been the ground conductors touching the signal conductor only when flexed a certain way. Of course, "touch it where it hurts" debugging like that can be risky to your system... ideally, you have an old receiver+source, and some dusty old speakers somewhere so you can test them in a parallel system.
If the terminations unscrew, visually inspect the terminations/solder work.