The 'classic' method to make that sort of worm gear arrangement "anti-backlash" is to cut the gear from two thin sheets of metal (as if one piece). Then mount one of them rigidly on the shaft, and mount the other snugly against the first with a clamping collar, but 'freely rotating'.
Then the free half-slice is strongly spring-loaded radially against the fixed one, such that the teeth pinch the worm between the two half-gears' (now slightly mis-aligned) teeth. The maximum torque allowed before backlash returns is determined by the strength of the spring.
Lloyd