Shortly after, I put 2 and 2 together and moved my cue under my left eye. Now, I'm dead center on the cueball and it actually looks dead center.
This is exactly the illusion that was fixed for me too. I would line up a ball center-to-center and it wouldn't "look" center to center. My mind had to make up for the difference. I had to guess at the shot. Over time the guess got better and better, but some days it would be further off than others.
When I got my left eye over the shot, now center-to-center "looks" like center-to-center. No more guessing!