Have you done the camera calibration?
Using set focus with a calibrated machine usually results in alignment within a few millimeters.
You might also watch the set focus process in the machine and, make sure the targeting laser dot actually lands on your hanger. With a small target area, sometimes it will miss and measure off the edge.
A thing you could do to reduce waste would be to put some masking or something over the area you plan to engrave and, do a “practice” run at a low power that won’t pierce the masking. Then, you can see where the engrave will hit and, make adjustments before committing to engraving your hanger.