As long as the diffs are set on the bench not to slip and the grub screw is locked down, there is no way it can slip in the car. I would remove them, clean re-grease and re-adjust on the bench.
It doesnt matter which side you put the screw head on, its locked down by the grub screw. I've defied the odds for years and ran the screw head on the right side of every car I've owned without any diffs mysteriously loosening
