A lot of conventional pistol shooters have found training themselves to shoot left-handed is a good exercise just because you don't have flinches or other bad habits drilled into the weak side. I am not cross-dominant, but I find my left finger is easier to isolate from other minor muscle and tendon movements in the palm, so this is another advantage.
One tool that should be mentioned in more detail is the pistol shooter's hat. This is a baseball style
hat with a very long bill and flaps that dangle from either side of the bill. The flaps have Velcro strategically placed so you can position the flaps to form a tunnel for an eye to look through if you choose to.
The best batters in baseball are often cross-dominant. Dominant hand behind the bat, dominant eye on the pitcher. There seem to be enough of you on this board to get at least a softball league started.