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

I agree with onhwy61.  I think it has much to do with the mix of in phase and out of phase sound (too much out of phase info), but would add that whether or not it is an issue might well depend on your room and speaker set up. It does in mine anyway.

 For example in a recent record which was music of a centered vocalist and a small group (jazz) the vocalist was very sharply focused a foot or two left of center. (My speakers are set up triangulated about 9' apart and 10' from the listening chair with the axis of the speakers crossing just in front of my head. When I centered the image by shifting my chair to the right about 6 inches I lost a little bit of sharpness but it was still very good. When I shifted my chair another 6" (or more) to the right the voice went out of phase with no center image. When I listen to 'well recorded' music the image now shifts just slightly right but it is not as distracting nor is it particularly soft focused.

FWIW.

Is your turntable level? Is the cartridge properly aligned? Are there any issues with the pickup arm leads binding, or any issues with the pickup arm bearings? Is the stylus pristine and clean? Do you have this problem with sources other than LP?

Some details on your system might be helpful.

#3 and #4!

If you listened to the group in person, the singer usually moves around also.

Recordings are not like real life, and maybe the person doing the recording mix was not listening in the center, between the speakers.  Not all vocals are in the center, on every Lp.

The cutting head on the master lathe was installed by hand. It would be nice to think every human installing this head installed it perfectly perpendicular. The act of tightening said head to the lathe was done with screws. yada yada yada.

Your stylus diamond was installed by hand, human hands.

Album thickness means VTA is perfect on some albums, and off on others. etc. etc. etc.

Stop your obsession. Enjoy the music.

Here's something that may make no sense. If you have everything perfectly setup. If you have a really good system. If all the stars are aligned.  What happens when the singer moves their head, this in the middle of a song. Does your system accurately reproduce the now moved center of the singers vocal cords.

Stop your obsession. Enjoy the music.

Mine does this and I have thought of several factors.  Wear of the record, tubes' gain changing, system warmup, differences in tracking different parts of the record, volume control mistracking at various settings.  I have a preamp with separate volume controls so this is rarely a problem I cannot fix but could be annoying with the lack of this.  Getting this right greatly improves my soundstage.