Balance control?

I experience the same issue on some of my recordings.  Some simply don’t have a solid and stable center image; very frustrating.  At this point I would take some of those recordings to your friends’ and see if the same thing happens on their systems.  Good luck.

It is unwise to judge channel balance based on “perfect” centering of a vocalist.  You have no idea what the sound engineer was after when he set up the recording session or what sort of mixing was done.  Very often, the vocalist appears to be standing just to the left of center, near to the piano, in a jazz recording.  With the bass, drums, and etc to the right or behind the vocalist.

Balance control is a tricky thing. You have to consider if, for instance, the vocalist was standing slight to the right or left of the mic 

Yep, don't count on recordings always having perfectly balanced center image. I especially hear this with 60's recordings when stereo first became ubiquitous, engineers really liked to play with panning, separation, often hear vocalists slightly off to left. Seems like this was common practice, vocalist slightly off to right very rare.

Mono recordings can also expose an off center balance.  Play lots of mono recordings, you should have equal fill on both sides of the center. Try for the nicer mono recordings, those with wider perspective, crap mono recordings very narrow center image.

Stereo recordings can throw one off here, engineers, producers can do some pretty strange things.

Starting with the recorded vinyl record:

Not all have symmetrical balance.

Room placement, toe in, wall reflections can all influence balance.

At the turntable/ tonearm:

Antiskate, correct orientation of cartridge, Azimuth all will have a large influence. One cannot expect exact channel balance with inexact cartridge set up incorrect antiskate or azimuth.

The cartridge:

Ultra inexpensive cartridges cannot be expected to be as precisely accurate with regard to cartridge body to internal generator alignment. Costs are cut. So too are corners in quality..