If it makes you feel any better, when I was in boot camp, we had a day in the shooting range, which was one of those indoor-types you see on police movies, with paper targets deployed and retrieved by a rope and pulley system. Like your exercise, the weapon was a .22 pistol. I finished my firing exercise, then got to watch others take their turns from the side. One guy got everyone's attention, because a quick glance showed that he was aiming up at at least a 30-degree angle, and his shots were causing sparks on the pulley, several feet above the target.
I don't think a modified grip can fix that.
I never had any particular issues with pistols, because when I hold it out properly, it feels natural and easy to adjust a right-handed grip to line up with my left eye. Rifles and shotguns are another story, since I have to use them in the off hand. It's particularly problematic in a standing position... the heavier the weapon, the louder my body tells me to "move it to the strong side, stupid!"
