Excellent project.
The cutter is starting and running OK without an active Z axis height control, yes?
There seems to be some error between when the cutter is moving away from the camera vs toward camera. I noticed what looks like (nearest the camera) a flat (cord) on the round hole and the two short segments of the square don't converge. Are those intended or mechanical backlash or software tuning? My question is, if those observances aren't intended, where do you expect to implement the fix?