I am in the same situation.
After a few years of working on it your best solution is to ALWAYS aim with both eyes open.
With a rifle, using a RDS, it's easy. Basically look at your target only, then position your rifle/body to put the dot on your target (not the other way around). You get great target aquisition that way.
With a scoped/zoomed optic, it's really hard, but with traning it works. You basically will see everything with your left/dominant eye, except a round "zoomed" zone, very much like some video games work. At first, the image will move around/blur. Keep focusing on you target, and the zommed image will become clear, with the background/surroundings blurry. It's good enough to see movements/not get flaked.
For pistols, I don't remember the name of the stance I use... basically you hold your pistol with your right hand. Position yourself facing right of the target, then bring your right arm across your chest and sight with you left eye. The pistol ends-up vertical, no angle, your profile is a lot smaller and your right eye gives you incredible surrouding awareness. You won't see two sets of sight because your noze bridge prevents your right eye from seeing your pistol.
Originally Posted by Drake
Damnit, don't make me add "no discussing temporal paradoxes" to the rules or I'll go back in time and ban you last week.