That might work, assuming both one-sided discs measured 3.13mm. On my diff, there was 0.10mm difference from right to left, and you need to install different thicknesses on each side. Otherwise the left may be tighter than the right, or vice-versa. Just make sure you can get it to rotate on the bench, before installing in the car. I would avoid liquid additives if at all possible, I'd only try that as a last resort before re-opening the diff.