OK. Engineer here. Not quite following your description of the gear reversal and how that 'fixes' the problem, so maybe I'm missing something critical, but:
I don't think reversing (or simply rotating, if that's what you're suggesting) the exposed white gear 180 degrees will correct the problem. Yes, that could re-position a 'good' portion of the black gear onto the worm gear, but regardless of how the gears are positioned, as all of them turn, the black gear will rotate until its worn portion reaches the worm gear, then it stops turning again. This will happen within one rotation of the black gear.
Based on the wear that you highlighted on the black gear, I think it would have to be replaced -- if one can find the part...
X3 w/6-speed & Sport Package:
A sports sedan disguised as an SUV...