You might look at Center Axis Relock (google it, youtube it) as it has a rather interesting method of dealing with dual sight picture and it might make it easier to train your eyes to deal with it in more traditional stances.
Caveat: I've never been trained in CAR, I've just seen it described and demonstrated. YMMV.
It takes a little getting used to, especially if you've been shooting with the other eye closed. Absolutely no question about that. Once you get it down, though, you get to where you can't really tell the difference. There's none of the ghost images or bluriness.
The one I have trouble with is not blinking. It's a natural reflex, so it's hard to keep from blinking when the gun goes boom.
I noticed that blink/flinch reflex with pistols as well, and I remember when I was younger and shooting skeet at summer camp, the instructor CONSTANTLY berated me for it, (even though I ended up winning third prize in the skeet competition that year). I didn't think I could do anything about it.
I discovered something interesting when I started reloading. I was testing out a problematic batch, and was watching the cases as they came out of the gun. The batch was loaded a little light, and the shells were mostly just "dribbling" out of the gun instead of ejecting with any real authority. I wasn't focused on any particular target, just firing into the side of a hill and paying attention to how well the gun was handling the reloaded shells. It wasn't until later that I realized that if I was watching them as they ejected, I couldn't have been blinking as it happened.
My suggestion to you is to try point-shooting. Don't sight the gun, just point at a silhouette target at 10 to 15 feet and pull the trigger. Try doing as I did, and focus on the shell ejecting instead of the gun going bang, and you should be able to overcome that flinch pretty quickly. You might try some quick double taps, see if you can observe both cartridges as they eject. If you can observe the shells as they eject and begin their arc out to the right, you can't be flinching, and you should be able to get from there to flinchless sighted fire pretty easily.