I've come across this problem before when teaching archery, in which it is if anything far harder to retrain someone to shoot with their off hand.
The best solution seems to be to use both eyes open to assess the range, then close the dominant off hand eye to take the shot.
You may need an extended period of practice to stop yourself forgetting to close your dominant eye, but there is the advantage that with modern optics you can adjust your scope to perfect focus with your weaker eye, so you shouldn't end up at any disadvantage.
Chris.