Is it possible for the center image to drift from lp to lp?

I have noticed this with numerous LP's.  I think the absolute phase between L & R channels is crap shoot in the long, arduous rendering of the recording from the master tape to the cutter lathe to the master to the stamper to the record. It only takes a couple microns of displacement from inner to outer walls of the groove to screw this up.

The solution is actually pretty easier - get and use a good balance control.  The ear will ignor the phase difference and center the image based on amplitude with just a minor adjustment (about in 1-2 dB) in L/R balance.

BTW, I've never heard this effect on a digital recording - they all seem to be consistent in this regard on my system.

Astro58go, if you are handy with a soldering iron, get a small box and and Alps RK40 (Black Beauty) balance pot.  These are the best pots ever made (IMHO), and are still readily available on eBay.  Put a set of input and output jacks on the box and use the box between your preamp and power amp, where it will make the least impact on sound quality.  There is a detent on the pot to know when you have equal gain on both sides.  You only need to make a small adjustment to center the image of any LP.  Total investment, including the pot, is about $150.00 !