Couple of things you can try.
First, take the drumsticks out of the jig while you’re snapping, you can place them after the design has been snapped. (Make sure you have the jig anchored down. You don’t want it to shift.)
Make sure when you snap to the snapmarks, that you are using the height of the jig material in the Unknown Materials slot, not the height of the sticks.
When you do the snapping, look down on the machine bed, watch closely, and make sure that the little red dot during the auto-focus process is landing on the jig, and not off to the side. You have the snapmarks awfully close to a “dropoff” on both sides. Leaving a little more space to the left and right of the printed snapmarks on your jig might take care of the problem. (Or you can run a strip of tape around the outside of the jig so the beam doesn’t fall off the edge into the grid.)
If you do get a successful snap, open the lid, put the sticks in the holes, then do one more thing. Change the focal point for the engrave operation to match the height of the sticks. (Change it in the Manual settings area.)
I think all you’ll probably need to do is cut a new jig and leave more space between the edges and the snapmarks.
And you might want to read through these notes.