Most people, whether they aim using the arrow point or shoot instinctively, get used to the center cut on the bow they normally shoot, and if they switch to a bow with less center cut, they will shoot left (RH shooters), and vice versa. Since I shoot a number of bows regularly, and don't want to have to keep getting used to different center cuts, I now only buy bows with more or less the same center cut I’m used to.
If I shoot a Hill bow, I will shoot left. The best way for me to become accustomed to this is to expand my aiming awareness beyond the arrow point to the whole arrow shaft. If I do this, I can see that it is pointing left, and make the necessary correction. I could probably do the same thing by playing around with cant, but I don't want to limit myself to a particular cant.
If I were an instinctive shooter, I would just have to wait until my brain re-programmed to the new center cut. I could help the process along by using a softer strike plate, like rug rest material, which moves the POI to the right, but often bows not cut to center also don't have a very generous rest area, so taking up some of that valuable real estate with a rug rest might make it too crowded.