LP's: the measure of off-centre record spindle holes ?

Well I said hopefully.

When an off-center lp rotates, as the cartridge sees it in real time there’s a slight speed offset, IMO. Therefore any cause of speed irregularity could possibly be corrected by a device such as the Eagle/Roadrunner that constantly monitors speed at every rotation.

Maybe a better way to say it is any deflection (tracing error) regarding the cartridge/arm’s ability to trace the lp perfectly will cause some speed irregularity. This is of coarse after I've reamed out off-center records to the best of my ability as stated above.

slaw

When an off-center lp rotates, as the cartridge sees it in real time there’s a slight speed offset, IMO. Therefore any cause of speed irregularity could possibly be corrected by a device such as the Eagle/Roadrunner that constantly monitors speed at every rotation ...

The Eagle/Roadrunner works by monitoring platter speed, so it will be of no help with an LP that has an off-center hole. That’s because the LP with off-center hole can’t affect platter speed, but only the effective speed of the phono cartridge as it tracks the eccentric disc.

Cleeds is right slaw. The feedback signal is taken from the platter not the record. 
If it bothers me I take the record back and get another copy.

Points taken. They make sense. I was hoping it would be an added benefit over and above. Thanks guys.

I usually notice this audibly, especially with piano or sustained strings, and it drives me nuts!

If not too bad, a workaround is to slightly enlarge the center hole with a reamer tool and reposition.  Do this away from the turntable and carefully brush away any vinyl scraps.  Return the record to the turntable centered by eye on spindle and hold in place with a reflex clamp.  Note where tonearm has greatest excursion from center, lightly mark the direction on the label with pencil (or post-it style flag).  Remove clamp and push record against spindle at that location to correct, and re-clamp.  Sometimes a few iterations are needed.  Next time you play the record, you can just look for your pencil mark.

Important:  The eccentricity not correlated between the the two sides, so this process needs to be repeated on the other side.  Usually the production hole is well centered in the vinyl, but somehow the master with the grooves wasn't aligned when pressed.