What you need is to scale down the tolerances. To remove the wiggle room.
One of the solutions that does not add a bias that I remember is two identical flat gears on the same axis with a spring that tries to rotate them one relative to another. This removes the wiggle room between this composite gear and the next, regular gear. The motor may have wiggle room, but the gears (which carry angle sensors, don't they?) move without wiggling, and react immediately as you reverse the direction. The load is limited though: the beating surface is twice as small, and the friction is higher.