3D 2 Sides Carve not lining up

Trying a two sided 3D carve and I can’t seem to get both halves to line up correctly.

I would ask do you have a fixture to keep the work in place? Is everything square and calibrated? Is the work square to begin with? Is there any flex to anything?

Since you are flipping the work, I would designate the origin on your drawing as the same place as your home switch. Then after carving one side, go back and home again for the second side. I would flip on the Y axis myself.

You could also put drill holes to put pins in a jig/fixture to orient the work on the centerline.This is an STL on the net as I don’t have Pro to save your work.