You main problem, as you have correctly identified, is the difference in centershot between your recurve and your longbow. Most people have the same problem as you do when they switch from a recurve that is cut past center to a longbow that is cut short of center. If you stay with the longbow long enough, you will adjust, and then if you switch back to a recurve, you will have to adjust all over again. Some people seem to have the knack of going back and forth between bows with different centershots, but I am not one of them, so I stick with recurves and longbows that are cut to more or less the same centershot
I would not worry as much about hitting low, as long as you are consistent. You should be able to easily correct this by moving to a slightly lower anchor, or possibly lowering your nock point, if there is any room to lower it before you begin to have clearance issues or porpoising. Again, this will take care of itself in time if you stick with this bow, just like the left misses will.
You can move the POI to the right by using a softer strikeplate or experimenting with different arrow spines and point weights. If you want to speed along the natural process, look where your arrow is pointing when you are at full draw, not just at the point but along the whole length of the arrow. You will probably notice that your arrow is pointed left of where you think it is. You can make a slight correction by swiveling at the hip, without wrecking your form by moving your arms or shoulders. I find that if I do this a few times, I can learn where I have to hold my bow so the arrow flies straight, even though it feels like I’m holding it too far right. Eventually that feeling will go away, and things will feel normal again.