Using the laser edge finder is the problem. They are not accurate enough to reset or place the origin to the center of an existing hole. Between the beam width and exponential runout the farther above the edge, the worse it can influence human error. I wouldn't trust one expecting under .015 position tolerances.
Use an indicator in or on the spindle to reference the origin to your part. You can find indicator holders like the Indicol clamp or tool holder mounted style. The indicator resolution may also be of importance. If you expect finer than .001 centering, use a .0001 resolution indicator. Once you have the indicator pointer stable at four quadrants of the bore, boss or hole, set your origin and you should be good to go within the capability of the machine.
I should also add that it is essential to check your head is trammed in to the table. If the head is not true perpendicular, there will be a mis-alignment from where the origin is set to where the cutter actually places the next cut(s) if the Z distance changes between tools. Not to mention the new feature at an odd angle of what is expected.