I am also cross-eye dominant, right-handed. I've done a bit of personal research on this myself. Every handgun I've ever owned (12 in all), I've shot slightly to the left, a little low maybe, but definitely more to the left, even at seven yards. With Glocks, I push the rear sight to the right to try to compensate.
When I got my HK P7M13, I immediately loved it, especially compared to my G19 and G34, because the trigger is about 4 pounds, and although it has a much longer reset, it doesn't stack at all like the Glock, it is smooth and does not have much play. A couple of weeks ago, after 2 weeks of dry-fire practice, I was consistently shooting dead on for the first time, with 5-6" 50 round groups at 25 yards offhand. It was by far the best I've ever shot, and the people around me were pretty impressed as well, a good feeling for me. Two days later, I went and shot so more, with the same results, itty-bitty groups in targets and gaping bystanders. All was well.
Then when I went out last week, I sucked huge, everything again to the left and groups twice as big as the week before. That week had been hectic at work, and I didn't get my usual reps of dry-fire. Frustrated, I kept at it that day trying to get back in the groove, even buying another 200 rounds for a total of 600 rounds shot. That didn't help, and what I find is there's only so long I can focus, and I was past that point of diminishing returns.
But I know that I'll do well again, because I have the fix, if I can just execute, or course. To me, the issue is not necessarily a cross-correction or any kind of a visual problem, although being cross-dominant might complicate things (I personally find myself canting the gun, especially one handed), but rather something else.
In my opinion, the main problem is grip and hand pressure, that of my fingers of the dominant hand tightening up as I pull the trigger, "mashing" the trigger, so to speak, basically, pulling the gun off-line during trigger pull.
Pulling with less of the finger on the trigger, with just the pad, will help this. Using a wedge grip, in other words, with the support index finger far ahead on the bottom of the trigger guard (doesn't work well on the Steyr, but works for me on P7 and Glock) helps control the lateral deviation. Using the thumbs-forward grip, illustrated so well by IDPA Steyr in a great post in Glocktalk, helps. Lots of dry fire helps. Concentrating on smoothness before speed helps. Relaxing your shooting hand starting at the thumb (which is helped by the thumb forward grip) is key. Going to the range with a plan more than blowing off a few hundred rounds is imperative.
Blindly mixing in snap caps with live ammo helps a TON. Try first mixing rounds in blindly in a box, then not looking while you load. If you haven't tried that already, it might be very revealing to find out how you're pulling the trigger when you know the gun is actually going to go off, as opposed to the nice, straight, smooth pull that you accomplish with boring regularity during dry fire when you know the gun is not going to go off. Personally, I was shocked to find out how much the gun was moving when I pulled the trigger on a snap cap. After doing that drill, I took it another step and alternated live rounds and snap caps through a few magazines. That helps program pulling the trigger the right way every time, one live, one not. One live, then one not. Concentrating on using the same pull, focusing on the front sight the whole time. A good thumbs-forward hand position can help control the degree of lateral movement, but the bottom line is that you have to pull the trigger straight back, with smooth, even, consistent pressure. Not 15 pounds of pressure to pull a 4 pound trigger, but 5-7 pounds of pressure. Again, relaxing your shooting hand is essential.
Some of the top shooters in the world will slap as they pull, in other words, between shots their trigger finger will totally lose contact with the trigger. However, they have found a way (through practice) to pull in such a way that the finger comes with just enough pressure applied in a straight back fashion, not laterally throwing the gun off line. I find it interesting that some of the best pistol shooters in the world have learned to move their trigger fingers a great deal more than seems necessary on purpose. I think they do it to ensure even pressure, a straight-back pull, and is their way of intentionally not staging the trigger, which shooters love to do but may not be the best idea. Why? Because for many, when the shooter stages the trigger, IE, the finger stops movement until the desired sight picture is found, they then mash the trigger and anticipate the shot. Concentrating on bringing even, smooth pressure all the way back works better for me.
Like so many things in life, it's much easier to think about doing things the right way then actually doing them. But of course, practice with purpose is the key.
I've also found that guns like 1911's, P7's, and Steyrs are easier for me to shoot than Glocks and any conventional Double Action, which is why I'm selling my two Glocks and am getting an Steyr S9 and M9.
With Glocks, for example, the pull is pretty light but it stacks at the end, making the ideal surprise break more difficult and therefore mash, flinch, etc., are definitely more of a factor. And with DA like Sig, HK USP, etc., the pull is so long and heavy that I find it's a detriment in general, I have to concentrate harder and my groupings aren't as good.
Now, it can be argued that I should be able to learn a trigger given practice, but a friend brought up an excellent point at the range when I was agonizing about dropping thousands on a P7 (now I have 2, 3k worth of two guns!) after finding that I immediately shot better with it then my practical, economical, durable, easy to service Glocks. I was saying that I should just learn how to shoot the Glock as well instead of just buying a gun, etc, and he said, "you should never have to overcome the trigger on a gun." He's right. Why do we shoot some guns better than others? Have you ever picked up a gun and shot it better than guns that you shot tens of thousands of rounds with? It might be because you haven't shot the gun enough to know where in the trigger pull it's going to go off when you pull the trigger, and therefore you get the ideal surprise break. I personally believe that the quality of the trigger is as important as any other factor when picking a gun to shoot well.
After shooting and becoming spoiled by my 2 P7's, I find that I just don't want to shoot my Glocks anymore. The only modern design I've tried that comes close is the Steyr, although the XD is nice as well. But the XD just doesn't fit my hand as well as the Steyr, and the trigger on the Steyr is shorter and very crisp. Every time I go the range with my buddy who I sold my M40A-1 to, I regret it, especially when I get to shoot it. I can't wait to get these guns, can you tell?
Big long post, I hope that helps.