I'm not surprised there is a left-right difference when going form a tab to a release. I would actually expect to see some difference.

I don't put much stock in paper tuning. Has the bow been walk-back tuned? If not, do that first. You may find the rest needs to be moved to the left. Don't worry if the arrow does not look "centered" along the string or when looking at the limbs. Centershot is different for every shooter.

If the rest needs to be moved left, that is a big part of the problem.